How can I show radius of this circle exactly?Issue with Expansions of Nested MacrosHow do I split large numbers into groups of five digits?How can I automatically calculate sums in a LaTeX table?How can I nest coordinate calculations in TikZ?How to translate this scenario to LaTeX looping macro?How can I show base-2 long division?How can I convert units in LaTeX environment?How can I multiply two numbers?How can I illustrate point decimal number to binary conversionHow can I calculate geometric sequence in LaTeX?
Is the Amazon rainforest the "world's lungs"?
Notice period 60 days but I need to join in 45 days
What should be done with the carbon when using magic to get oxygen from carbon dioxide?
Within what limits can the prime minister ask the queen to prorogue parliament?
Spicing up a moment of peace
Employing a contractor proving difficult
Did the Apollo Guidance Computer really use 60% of the world's ICs in 1963?
Why didn't Doc believe Marty was from the future?
How did medieval manors handle population growth? Were there room for more fields to be ploughed?
Is this password scheme legit?
Should I use the words "pyromancy" and "necromancy" even if they don't mean what people think they do?
Are spot colors limited and why CMYK mix is not treated same as spot color mix?
Why can't you say don't instead of won't?
Cutting numbers into a specific decimals
Are sweatpants frowned upon on flights?
Why is there no Disney logo in MCU movies?
Fantasy Macro Economics: What would Merfolk trade for?
Is the internet in Madagascar faster than in UK?
Term used to describe a person who predicts future outcomes
How could a self contained organic body propel itself in space
Can someone identify this unusual plane at airport?
What to do about my 1-month-old boy peeing through diapers?
Did ancient peoples ever hide their treasure behind puzzles?
Why nature prefers simultaneous events?
How can I show radius of this circle exactly?
Issue with Expansions of Nested MacrosHow do I split large numbers into groups of five digits?How can I automatically calculate sums in a LaTeX table?How can I nest coordinate calculations in TikZ?How to translate this scenario to LaTeX looping macro?How can I show base-2 long division?How can I convert units in LaTeX environment?How can I multiply two numbers?How can I illustrate point decimal number to binary conversionHow can I calculate geometric sequence in LaTeX?
.everyoneloves__top-leaderboard:empty,.everyoneloves__mid-leaderboard:empty,.everyoneloves__bot-mid-leaderboard:empty margin-bottom:0;
7
I want to show radius of this circle. The correct result of radius is 7/sqrt(3). My code.
documentclass[border = 1mm]standalone
usepackagetikz
usepackagetikz-3dplot
usetikzlibraryintersections,calc,backgrounds,fpu
newcommandPgfmathsetmacroFPU[2]begingroup%
pgfkeys/pgf/fpu,/pgf/fpu/output format=fixed%
pgfmathsetmacro#1#2%
pgfmathsmuggle#1endgroup
begindocument
tdplotsetmaincoords7080
begintikzpicture[tdplot_main_coords,line join = round, line cap = round]
pgfmathsetmacroa5
pgfmathsetmacrob7
pgfmathsetmacroc8
PgfmathsetmacroFPUmyrsqrt(-
pow(a,2) *pow(b,2)* pow(c,2)/ (pow(a,4) + pow(b,4) + pow(c,4)- 2
*pow(a,2) *pow(b,2) - 2*pow(c,2) *pow(b,2)-2*pow(c,2) *pow(a,2) ))
coordinate (A) at (0,0,0);
coordinate (B) at (c,0,0);
coordinate (C) at ((pow(b,2) + pow(c,2) - pow(a,2))/(2*c),sqrt((a+b-c) *(a-b+c) *(-a+b+c)* (a+b+c))/(2*c),0);
coordinate (T) at (c/2, c* (a*a + b*b - c*c)/(2*sqrt((a+b-c) *(a-b+c)* (-a+b+c)* (a+b+c))),0);
foreach point/position in A/left,B/below,C/right,T/below
fill (point) circle (1.8pt);
node[position=3pt] at (point) $point$;
beginscope[canvas is xy plane at z=0]
draw[thick] (T) circle (myr);
endscope
pgfmathparsemyr
pgfmathresult
endtikzpicture
enddocument
I tried
pgfmathparsemyr
pgfmathresult
I can't obtain the result. How can I get the result automatically (not by hand)?
calculations
asked Aug 16 at 4:34
minhthien_2016minhthien_2016
2,2531 gold badge12 silver badges19 bronze badges
|
show 3 more comments
7
I want to show radius of this circle. The correct result of radius is 7/sqrt(3). My code.
documentclass[border = 1mm]standalone
usepackagetikz
usepackagetikz-3dplot
usetikzlibraryintersections,calc,backgrounds,fpu
newcommandPgfmathsetmacroFPU[2]begingroup%
pgfkeys/pgf/fpu,/pgf/fpu/output format=fixed%
pgfmathsetmacro#1#2%
pgfmathsmuggle#1endgroup
begindocument
tdplotsetmaincoords7080
begintikzpicture[tdplot_main_coords,line join = round, line cap = round]
pgfmathsetmacroa5
pgfmathsetmacrob7
pgfmathsetmacroc8
PgfmathsetmacroFPUmyrsqrt(-
pow(a,2) *pow(b,2)* pow(c,2)/ (pow(a,4) + pow(b,4) + pow(c,4)- 2
*pow(a,2) *pow(b,2) - 2*pow(c,2) *pow(b,2)-2*pow(c,2) *pow(a,2) ))
coordinate (A) at (0,0,0);
coordinate (B) at (c,0,0);
coordinate (C) at ((pow(b,2) + pow(c,2) - pow(a,2))/(2*c),sqrt((a+b-c) *(a-b+c) *(-a+b+c)* (a+b+c))/(2*c),0);
coordinate (T) at (c/2, c* (a*a + b*b - c*c)/(2*sqrt((a+b-c) *(a-b+c)* (-a+b+c)* (a+b+c))),0);
foreach point/position in A/left,B/below,C/right,T/below
fill (point) circle (1.8pt);
node[position=3pt] at (point) $point$;
beginscope[canvas is xy plane at z=0]
draw[thick] (T) circle (myr);
endscope
pgfmathparsemyr
pgfmathresult
endtikzpicture
enddocument
I tried
pgfmathparsemyr
pgfmathresult
I can't obtain the result. How can I get the result automatically (not by hand)?
calculations
asked Aug 16 at 4:34
minhthien_2016minhthien_2016
2,2531 gold badge12 silver badges19 bronze badges
E.g.draw (T) -- (C) node[midway,sloped,fill=white] $pgfmathprintnumbermyr$cm;.
– Schrödinger's cat
Aug 16 at 5:03
@Dunno This is an approximate result. Can I get exactly result?
– minhthien_2016
Aug 16 at 5:07
pgfmathparsemyr xdefrpgfmathresult $r cm$
– koleygr
Aug 16 at 5:23
@koleygr The approximate about4.0414518843273803516. I want to exactly result.
– minhthien_2016
Aug 16 at 5:27
1
@koleygr Yes.frac73cdotsqrt3.
– minhthien_2016
Aug 16 at 5:31
|
show 3 more comments
7
7
7
I want to show radius of this circle. The correct result of radius is 7/sqrt(3). My code.
documentclass[border = 1mm]standalone
usepackagetikz
usepackagetikz-3dplot
usetikzlibraryintersections,calc,backgrounds,fpu
newcommandPgfmathsetmacroFPU[2]begingroup%
pgfkeys/pgf/fpu,/pgf/fpu/output format=fixed%
pgfmathsetmacro#1#2%
pgfmathsmuggle#1endgroup
begindocument
tdplotsetmaincoords7080
begintikzpicture[tdplot_main_coords,line join = round, line cap = round]
pgfmathsetmacroa5
pgfmathsetmacrob7
pgfmathsetmacroc8
PgfmathsetmacroFPUmyrsqrt(-
pow(a,2) *pow(b,2)* pow(c,2)/ (pow(a,4) + pow(b,4) + pow(c,4)- 2
*pow(a,2) *pow(b,2) - 2*pow(c,2) *pow(b,2)-2*pow(c,2) *pow(a,2) ))
coordinate (A) at (0,0,0);
coordinate (B) at (c,0,0);
coordinate (C) at ((pow(b,2) + pow(c,2) - pow(a,2))/(2*c),sqrt((a+b-c) *(a-b+c) *(-a+b+c)* (a+b+c))/(2*c),0);
coordinate (T) at (c/2, c* (a*a + b*b - c*c)/(2*sqrt((a+b-c) *(a-b+c)* (-a+b+c)* (a+b+c))),0);
foreach point/position in A/left,B/below,C/right,T/below
fill (point) circle (1.8pt);
node[position=3pt] at (point) $point$;
beginscope[canvas is xy plane at z=0]
draw[thick] (T) circle (myr);
endscope
pgfmathparsemyr
pgfmathresult
endtikzpicture
enddocument
I tried
pgfmathparsemyr
pgfmathresult
I can't obtain the result. How can I get the result automatically (not by hand)?
calculations
asked Aug 16 at 4:34
minhthien_2016minhthien_2016
2,2531 gold badge12 silver badges19 bronze badges
I want to show radius of this circle. The correct result of radius is 7/sqrt(3). My code.
documentclass[border = 1mm]standalone
usepackagetikz
usepackagetikz-3dplot
usetikzlibraryintersections,calc,backgrounds,fpu
newcommandPgfmathsetmacroFPU[2]begingroup%
pgfkeys/pgf/fpu,/pgf/fpu/output format=fixed%
pgfmathsetmacro#1#2%
pgfmathsmuggle#1endgroup
begindocument
tdplotsetmaincoords7080
begintikzpicture[tdplot_main_coords,line join = round, line cap = round]
pgfmathsetmacroa5
pgfmathsetmacrob7
pgfmathsetmacroc8
PgfmathsetmacroFPUmyrsqrt(-
pow(a,2) *pow(b,2)* pow(c,2)/ (pow(a,4) + pow(b,4) + pow(c,4)- 2
*pow(a,2) *pow(b,2) - 2*pow(c,2) *pow(b,2)-2*pow(c,2) *pow(a,2) ))
coordinate (A) at (0,0,0);
coordinate (B) at (c,0,0);
coordinate (C) at ((pow(b,2) + pow(c,2) - pow(a,2))/(2*c),sqrt((a+b-c) *(a-b+c) *(-a+b+c)* (a+b+c))/(2*c),0);
coordinate (T) at (c/2, c* (a*a + b*b - c*c)/(2*sqrt((a+b-c) *(a-b+c)* (-a+b+c)* (a+b+c))),0);
foreach point/position in A/left,B/below,C/right,T/below
fill (point) circle (1.8pt);
node[position=3pt] at (point) $point$;
beginscope[canvas is xy plane at z=0]
draw[thick] (T) circle (myr);
endscope
pgfmathparsemyr
pgfmathresult
endtikzpicture
enddocument
I tried
pgfmathparsemyr
pgfmathresult
I can't obtain the result. How can I get the result automatically (not by hand)?
calculations
calculations
asked Aug 16 at 4:34
minhthien_2016minhthien_2016
2,2531 gold badge12 silver badges19 bronze badges
asked Aug 16 at 4:34
minhthien_2016minhthien_2016
2,2531 gold badge12 silver badges19 bronze badges
edited Aug 16 at 5:13
minhthien_2016
asked Aug 16 at 4:34
minhthien_2016minhthien_2016
2,2531 gold badge12 silver badges19 bronze badges
asked Aug 16 at 4:34
minhthien_2016minhthien_2016
2,2531 gold badge12 silver badges19 bronze badges
asked Aug 16 at 4:34
minhthien_2016minhthien_2016
2,2531 gold badge12 silver badges19 bronze badges
2,2531 gold badge12 silver badges19 bronze badges
E.g.draw (T) -- (C) node[midway,sloped,fill=white] $pgfmathprintnumbermyr$cm;.
– Schrödinger's cat
Aug 16 at 5:03
@Dunno This is an approximate result. Can I get exactly result?
– minhthien_2016
Aug 16 at 5:07
pgfmathparsemyr xdefrpgfmathresult $r cm$
– koleygr
Aug 16 at 5:23
@koleygr The approximate about4.0414518843273803516. I want to exactly result.
– minhthien_2016
Aug 16 at 5:27
1
@koleygr Yes.frac73cdotsqrt3.
– minhthien_2016
Aug 16 at 5:31
|
show 3 more comments
E.g.draw (T) -- (C) node[midway,sloped,fill=white] $pgfmathprintnumbermyr$cm;.
– Schrödinger's cat
Aug 16 at 5:03
@Dunno This is an approximate result. Can I get exactly result?
– minhthien_2016
Aug 16 at 5:07
pgfmathparsemyr xdefrpgfmathresult $r cm$
– koleygr
Aug 16 at 5:23
@koleygr The approximate about4.0414518843273803516. I want to exactly result.
– minhthien_2016
Aug 16 at 5:27
1
@koleygr Yes.frac73cdotsqrt3.
– minhthien_2016
Aug 16 at 5:31
E.g.
draw (T) -- (C) node[midway,sloped,fill=white] $pgfmathprintnumbermyr$cm;.– Schrödinger's cat
Aug 16 at 5:03
E.g.
draw (T) -- (C) node[midway,sloped,fill=white] $pgfmathprintnumbermyr$cm;.– Schrödinger's cat
Aug 16 at 5:03
@Dunno This is an approximate result. Can I get exactly result?
– minhthien_2016
Aug 16 at 5:07
@Dunno This is an approximate result. Can I get exactly result?
– minhthien_2016
Aug 16 at 5:07
pgfmathparsemyr xdefrpgfmathresult $r cm$– koleygr
Aug 16 at 5:23
pgfmathparsemyr xdefrpgfmathresult $r cm$– koleygr
Aug 16 at 5:23
@koleygr The approximate about
4.0414518843273803516. I want to exactly result.– minhthien_2016
Aug 16 at 5:27
@koleygr The approximate about
4.0414518843273803516. I want to exactly result.– minhthien_2016
Aug 16 at 5:27
1
1
@koleygr Yes.
frac73cdotsqrt3.– minhthien_2016
Aug 16 at 5:31
@koleygr Yes.
frac73cdotsqrt3.– minhthien_2016
Aug 16 at 5:31
|
show 3 more comments
1 Answer
1
active
oldest
votes
8
There is only very limited support for fraction detection and so on in pgf, and as soon as square roots are involved I think you do need to do some of the things by hand. (To be fair, computer algebra systems are also not great at detecting such expressions, but if you use those to parse the expressions then you can get exact result. Yet LaTeX is not such a computer algebra system.) You can use the keys
pgfkeys/pgf/number format/.cd,frac, frac denom=3,frac whole=false
to obtain
documentclass[border = 1mm]standalone
usepackagetikz
usepackagetikz-3dplot
usetikzlibraryintersections,calc,backgrounds,fpu
newcommandPgfmathsetmacroFPU[2]begingroup%
pgfkeys/pgf/fpu,/pgf/fpu/output format=fixed%
pgfmathsetmacro#1#2%
pgfmathsmuggle#1endgroup
begindocument
tdplotsetmaincoords7080
begintikzpicture[tdplot_main_coords,line join = round, line cap = round]
pgfmathsetmacroa5
pgfmathsetmacrob7
pgfmathsetmacroc8
PgfmathsetmacroFPUmyrsqrt(-
pow(a,2) *pow(b,2)* pow(c,2)/ (pow(a,4) + pow(b,4) + pow(c,4)- 2
*pow(a,2) *pow(b,2) - 2*pow(c,2) *pow(b,2)-2*pow(c,2) *pow(a,2) ))
coordinate (A) at (0,0,0);
coordinate (B) at (c,0,0);
coordinate (C) at ((pow(b,2) + pow(c,2) - pow(a,2))/(2*c),sqrt((a+b-c) *(a-b+c) *(-a+b+c)* (a+b+c))/(2*c),0);
coordinate (T) at (c/2, c* (a*a + b*b - c*c)/(2*sqrt((a+b-c) *(a-b+c)* (-a+b+c)* (a+b+c))),0);
foreach point/position in A/left,B/below,C/right,T/below
fill (point) circle (1.8pt);
node[position=3pt] at (point) $point$;
beginscope[canvas is xy plane at z=0]
draw[thick] (T) circle (myr);
endscope
draw (T) -- (C) node[midway,sloped,fill=white] %
pgfmathparsemyr/sqrt(3)%
pgfkeys/pgf/number format/.cd,frac, frac denom=3,frac whole=false%
$pgfmathprintnumberpgfmathresultcdotsqrt3,$cm;
endtikzpicture
enddocument
Of course, one can do better than that but to the best of my knowledge the routines for doing the required integer arithmetic are not yet implemented in pgf (and there is a slight chance that there is no real package for those). The main obstacle is that gcd, which is very useful to cancel common factors in fractions, does not yet work with fpu. On the other hand, you need fpu here because the numbers are so large. So I added variant of gcd (called gcdFPU) and a number of other routines such as integerpower which allows one to determine the power of a factor in an integer. For instance, integerpower(12,2) yields 2 since 12=2^2 times something that is not divisible by 2. This can be used to pull squares out of the square root.
documentclass[tikz,border=1mm]standalone
usepackagetikz-3dplot
usetikzlibraryfpu
newcounterifactor
newcommandPgfmathsetmacroFPU[2]begingroup%
pgfkeys/pgf/fpu,/pgf/fpu/output format=fixed%
pgfmathsetmacro#1#2%
pgfmathsmuggle#1endgroup
newcommandPgfmathtruncatemacroFPU[2]begingroup%
pgfkeys/pgf/fpu,/pgf/fpu/output format=fixed%
pgfmathtruncatemacro#1round(#2)%
pgfmathsmuggle#1endgroup
% the following functions are based on
% * https://tex.stackexchange.com/a/177109 (digitcount,digitsum,lastdigit)
% * https://tex.stackexchange.com/a/501895 (memberQ)
% or new in the sense that they were developed on the basis of the existing
% pgf functions
makeatletter
newcountc@Digits
newcountc@Powers
pgfmathdeclarefunctiondigitcount1%
begingroup%
globalc@Digits=0
expandafterDigitCount@i#1@nil%
pgfmathparseint(thec@Digits)%
pgfmathsmugglepgfmathresultendgroup
% defGroupDigits#1%
% globalc@Digits=0
% expandafterDigitCount@i#1@nil%
% pgfmathparseint(thec@Digits)
defDigitCount@i#1#2@nil%
advancec@Digits by @ne
ifxrelax#2relaxelseDigitCount@i#2@nilfi
pgfmathdeclarefunctiondigitsum1%
begingroup%
globalc@Digits=0
expandafterDigitSum@i#1@nil%
pgfmathparseint(thec@Digits)%
pgfmathsmugglepgfmathresultendgroup
% defDigitSum#1%
% globalc@Digits=0
% expandafterDigitSum@i#1@nil%
% pgfmathparseint(thec@Digits)
defDigitSum@i#1#2@nil%
advancec@Digits by #1
ifxrelax#2relaxelseDigitSum@i#2@nilfi
pgfmathdeclarefunctionlastdigit1%
begingroup%
globalc@Digits=0
expandafterLastDigit@i#1@nil%
pgfmathparseint(thec@Digits)%
pgfmathsmugglepgfmathresultendgroup
% defLastDigit#1%
% globalc@Digits=0
% expandafterLastDigit@i#1@nil%
% pgfmathparseint(thec@Digits)
defLastDigit@i#1#2@nil%
c@Digits=#1
ifxrelax#2relaxelseLastDigit@i#2@nilfi
pgfmathdeclarefunctionintegerpower2%
begingroup%
globalc@Powers=0%
pgfmathtruncatemacropgfutil@tmpa#1%
looppgfmathtruncatemacroitestgcd(pgfutil@tmpa,#2)%0
ifnumitest>1relax%
advancec@Powers by @ne%
pgfmathtruncatemacropgfutil@tmpapgfutil@tmpa/#2%
repeat%
pgfmathparseint(thec@Powers)%
pgfmathsmugglepgfmathresultendgroup
pgfmathdeclarefunctionintegerpower21% works with large numbers
begingroup%
pgfkeys/pgf/fpu=false%
globalc@Powers=0%
PgfmathtruncatemacroFPUpgfutil@tmpa#1%
loop%
pgfmathtruncatemacropgfutil@tmpblastdigit(pgfutil@tmpa)%
pgfmathtruncatemacroitestiseven(pgfutil@tmpb)%
ifnumitest=1%
advancec@Powers by @ne%
PgfmathtruncatemacroFPUpgfutil@tmpapgfutil@tmpa/2%
repeat%
pgfmathparseint(thec@Powers)%
pgfmathsmugglepgfmathresultendgroup
pgfmathdeclarefunctionintegerpower31% works with large numbers
begingroup%
pgfkeys/pgf/fpu=false%
globalc@Powers=0%
PgfmathtruncatemacroFPUpgfutil@tmpa#1%
loop%
pgfmathtruncatemacroitestdivby3(pgfutil@tmpa)%
ifnumitest=1%
advancec@Powers by @ne%
PgfmathtruncatemacroFPUpgfutil@tmpapgfutil@tmpa/3%
repeat%
pgfmathparseint(thec@Powers)%
pgfmathsmugglepgfmathresultendgroup
pgfmathdeclarefunctionmemberQ2%
begingroup%
edefpgfutil@tmpb0%
edefpgfutil@tmpa#2%
expandafterpgfmath@member@ipgfutil@firstofone#1pgfmath@token@stop
edefpgfmathresultpgfutil@tmpb%
pgfmath@smuggleonepgfmathresult%
endgroup
defpgfmath@member@i#1%
ifxpgfmath@token@stop#1%
else
ifnum#1=pgfutil@tmparelax%
gdefpgfutil@tmpb1%
fi%
expandafterpgfmath@member@i
fi
pgfmathdeclarefunctionisevenFPU1%
begingroup%
pgfmathparseiseven(lastdigit(#1))%
pgfmathsmugglepgfmathresultendgroup
pgfmathdeclarefunctionisoddFPU1%
begingroup%
pgfmathparseisodd(lastdigit(#1))%
pgfmathsmugglepgfmathresultendgroup
pgfmathdeclarefunctiondivby31%
begingroup%
pgfmathparsememberQ(3,6,9,digitsum(digitsum(#1)))%
pgfmathsmugglepgfmathresultendgroup
pgfmathdeclarefunctiongcdFPU2%
begingroup
pgfkeys/pgf/fpu=false%
pgfmathcontinuelooptrue
PgfmathtruncatemacroFPUpgfutil@tmpa#1%
PgfmathtruncatemacroFPUpgfutil@tmpb#2%
PgfmathtruncatemacroFPUitestifthenelse(pgfutil@tmpa==0,1,0)%
ifnumitest=1relax
pgfmathcontinueloopfalse
PgfmathtruncatemacroFPUpgfutil@tmpapgfutil@tmpb%
fi%
PgfmathtruncatemacroFPUitestifthenelse(pgfutil@tmpb==0,1,0)%
ifnumitest=1relax
pgfmathcontinueloopfalse
PgfmathtruncatemacroFPUpgfutil@tmpbpgfutil@tmpa%
fi%
PgfmathtruncatemacroFPUpgfutil@tmpaabs(pgfutil@tmpa)%
PgfmathtruncatemacroFPUpgfutil@tmpbabs(pgfutil@tmpb)%
loop
ifpgfmathcontinueloop%
PgfmathtruncatemacroFPUitestifthenelse(pgfutil@tmpa==pgfutil@tmpb,1,0)%
ifnumitest=1relax
pgfmathcontinueloopfalse
else
PgfmathtruncatemacroFPUitestifthenelse(pgfutil@tmpa>pgfutil@tmpb,1,0)%
ifnumitest=1relax
PgfmathtruncatemacroFPUpgfutil@tmpapgfutil@tmpa-pgfutil@tmpb%
else
PgfmathtruncatemacroFPUpgfutil@tmpbpgfutil@tmpb-pgfutil@tmpa%
fi
fi
repeat
PgfmathtruncatemacroFPUpgfmathresultpgfutil@tmpa%
pgfmathsmugglepgfmathresultendgroup
pgfmathdeclarefunctionfactorinteger1%
begingroup% not yet done
endgroup
makeatother
newcommandPgfmathfraction[3]begingroup%
pgfmathtruncatemacromynumerator#2/gcd(#2,#3)%
pgfmathtruncatemacromydenominator#3/gcd(#2,#3)%
pgfmathsmuggle#1endgroup
begindocument
tdplotsetmaincoords7080
foreach a/b/c in 3/4/5,6/7/8,5/7/8
begintikzpicture[tdplot_main_coords,line join = round, line cap = round,
declare function=numerator(a,b,c)=pow(a,2) *pow(b,2)* pow(c,2);
denominator(a,b,c)=-pow(a,4) - pow(b,4) - pow(c,4)+%
2*pow(a,2) *pow(b,2)+2*pow(c,2) *pow(b,2)+2*pow(c,2)*pow(a,2);]
beginscope[local bounding box=elli]
PgfmathtruncatemacroFPUmynumeratornumerator(a,b,c)
PgfmathtruncatemacroFPUmydenominatordenominator(a,b,c)
PgfmathtruncatemacroFPUmygcdgcdFPU(mynumerator,mydenominator)
messagenumerator=mynumerator,denominator=mydenominator,gcd=mygcd^^J
PgfmathtruncatemacroFPUnewnumeratormynumerator/mygcd
PgfmathtruncatemacroFPUnewdenominatormydenominator/mygcd
messagenew numerator=newnumerator,new denominator=newdenominator^^J
pgfmathtruncatemacromyprenum1
pgfmathtruncatemacromypreden1
foreach Prime in 2,3,5,7,11,13,17
pgfmathtruncatemacromyintintegerpower(newnumerator,Prime)
ifnummyint>1
pgfmathtruncatemacromyint2*int(myint/2)
PgfmathtruncatemacroFPUnewnumeratornewnumerator/pow(Prime,myint)
xdefnewnumeratornewnumerator
pgfmathtruncatemacromyprenummyprenum*pow(Prime,myint/2)
xdefmyprenummyprenum
fi
pgfmathtruncatemacromyintintegerpower(newdenominator,Prime)
ifnummyint>0
pgfmathtruncatemacromyint2*int(myint/2)
PgfmathtruncatemacroFPUnewdenominatornewdenominator/pow(Prime,myint)
xdefnewdenominatornewdenominator
pgfmathtruncatemacromypredenmypreden*pow(Prime,myint/2)
xdefmypredenmypreden
fi
messagenew numerator=newnumerator, pre num=myprenum,new
denominator=newdenominator, pre den=mypreden^^J
pgfmathsetmacromyr(myprenum/mypreden)*sqrt(newnumerator/newdenominator)
coordinate (A) at (0,0,0);
coordinate (B) at (c,0,0);
coordinate (C) at ((pow(b,2) + pow(c,2) - pow(a,2))/(2*c),sqrt((a+b-c) *(a-b+c) *(-a+b+c)* (a+b+c))/(2*c),0);
coordinate (T) at (c/2, c* (a*a + b*b - c*c)/(2*sqrt((a+b-c) *(a-b+c)* (-a+b+c)* (a+b+c))),0);
foreach point/position in A/left,B/below,C/right,T/below
fill (point) circle (1.8pt);
node[position=3pt] at (point) $point$;
beginscope[canvas is xy plane at z=0]
draw[thick] (T) circle (myr);
endscope
draw (T) -- (C) node[midway,sloped,fill=white] %
$displaystyleifnummypreden=1
myprenum
else
fracmyprenummypreden
fi
ifnumnewdenominator=1
ifnumnewnumerator=1
else
cdotsqrtnewnumerator
fi
else
ifnumnewnumerator=1
cdotfrac1sqrtnewdenominator
else
cdotsqrtfracnewnumeratornewdenominator
fi
fi,$cm;
endscope
node[above] at (elli.north)$a=a,b=b,c=c$;
endtikzpicture
enddocument
answered Aug 16 at 5:49
Schrödinger's catSchrödinger's cat
3,0515 silver badges13 bronze badges
I think, your answer is not automatically.
– minhthien_2016
Aug 16 at 5:58
Dunmo. I voted for your answer. But, your code doesn't true in every cases. E.G, triangle with lenght 6, 7, 8.
– minhthien_2016
Aug 16 at 10:34
Please try with sides 3, 4, 5. It is incorrect.
– minhthien_2016
Aug 16 at 10:36
Thank you very much.
– minhthien_2016
Aug 16 at 23:05
1
You can see package xintexpr.
– minhthien_2016
Aug 17 at 4:25
|
show 3 more comments
Your Answer
StackExchange.ready(function()
var channelOptions =
tags: "".split(" "),
id: "85"
;
initTagRenderer("".split(" "), "".split(" "), channelOptions);
StackExchange.using("externalEditor", function()
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled)
StackExchange.using("snippets", function()
createEditor();
);
else
createEditor();
);
function createEditor()
StackExchange.prepareEditor(
heartbeatType: 'answer',
autoActivateHeartbeat: false,
convertImagesToLinks: false,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: null,
bindNavPrevention: true,
postfix: "",
imageUploader:
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
,
onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
);
);
draft saved
draft discarded
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2ftex.stackexchange.com%2fquestions%2f504392%2fhow-can-i-show-radius-of-this-circle-exactly%23new-answer', 'question_page');
);
Post as a guest
Required, but never shown
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
8
There is only very limited support for fraction detection and so on in pgf, and as soon as square roots are involved I think you do need to do some of the things by hand. (To be fair, computer algebra systems are also not great at detecting such expressions, but if you use those to parse the expressions then you can get exact result. Yet LaTeX is not such a computer algebra system.) You can use the keys
pgfkeys/pgf/number format/.cd,frac, frac denom=3,frac whole=false
to obtain
documentclass[border = 1mm]standalone
usepackagetikz
usepackagetikz-3dplot
usetikzlibraryintersections,calc,backgrounds,fpu
newcommandPgfmathsetmacroFPU[2]begingroup%
pgfkeys/pgf/fpu,/pgf/fpu/output format=fixed%
pgfmathsetmacro#1#2%
pgfmathsmuggle#1endgroup
begindocument
tdplotsetmaincoords7080
begintikzpicture[tdplot_main_coords,line join = round, line cap = round]
pgfmathsetmacroa5
pgfmathsetmacrob7
pgfmathsetmacroc8
PgfmathsetmacroFPUmyrsqrt(-
pow(a,2) *pow(b,2)* pow(c,2)/ (pow(a,4) + pow(b,4) + pow(c,4)- 2
*pow(a,2) *pow(b,2) - 2*pow(c,2) *pow(b,2)-2*pow(c,2) *pow(a,2) ))
coordinate (A) at (0,0,0);
coordinate (B) at (c,0,0);
coordinate (C) at ((pow(b,2) + pow(c,2) - pow(a,2))/(2*c),sqrt((a+b-c) *(a-b+c) *(-a+b+c)* (a+b+c))/(2*c),0);
coordinate (T) at (c/2, c* (a*a + b*b - c*c)/(2*sqrt((a+b-c) *(a-b+c)* (-a+b+c)* (a+b+c))),0);
foreach point/position in A/left,B/below,C/right,T/below
fill (point) circle (1.8pt);
node[position=3pt] at (point) $point$;
beginscope[canvas is xy plane at z=0]
draw[thick] (T) circle (myr);
endscope
draw (T) -- (C) node[midway,sloped,fill=white] %
pgfmathparsemyr/sqrt(3)%
pgfkeys/pgf/number format/.cd,frac, frac denom=3,frac whole=false%
$pgfmathprintnumberpgfmathresultcdotsqrt3,$cm;
endtikzpicture
enddocument
Of course, one can do better than that but to the best of my knowledge the routines for doing the required integer arithmetic are not yet implemented in pgf (and there is a slight chance that there is no real package for those). The main obstacle is that gcd, which is very useful to cancel common factors in fractions, does not yet work with fpu. On the other hand, you need fpu here because the numbers are so large. So I added variant of gcd (called gcdFPU) and a number of other routines such as integerpower which allows one to determine the power of a factor in an integer. For instance, integerpower(12,2) yields 2 since 12=2^2 times something that is not divisible by 2. This can be used to pull squares out of the square root.
documentclass[tikz,border=1mm]standalone
usepackagetikz-3dplot
usetikzlibraryfpu
newcounterifactor
newcommandPgfmathsetmacroFPU[2]begingroup%
pgfkeys/pgf/fpu,/pgf/fpu/output format=fixed%
pgfmathsetmacro#1#2%
pgfmathsmuggle#1endgroup
newcommandPgfmathtruncatemacroFPU[2]begingroup%
pgfkeys/pgf/fpu,/pgf/fpu/output format=fixed%
pgfmathtruncatemacro#1round(#2)%
pgfmathsmuggle#1endgroup
% the following functions are based on
% * https://tex.stackexchange.com/a/177109 (digitcount,digitsum,lastdigit)
% * https://tex.stackexchange.com/a/501895 (memberQ)
% or new in the sense that they were developed on the basis of the existing
% pgf functions
makeatletter
newcountc@Digits
newcountc@Powers
pgfmathdeclarefunctiondigitcount1%
begingroup%
globalc@Digits=0
expandafterDigitCount@i#1@nil%
pgfmathparseint(thec@Digits)%
pgfmathsmugglepgfmathresultendgroup
% defGroupDigits#1%
% globalc@Digits=0
% expandafterDigitCount@i#1@nil%
% pgfmathparseint(thec@Digits)
defDigitCount@i#1#2@nil%
advancec@Digits by @ne
ifxrelax#2relaxelseDigitCount@i#2@nilfi
pgfmathdeclarefunctiondigitsum1%
begingroup%
globalc@Digits=0
expandafterDigitSum@i#1@nil%
pgfmathparseint(thec@Digits)%
pgfmathsmugglepgfmathresultendgroup
% defDigitSum#1%
% globalc@Digits=0
% expandafterDigitSum@i#1@nil%
% pgfmathparseint(thec@Digits)
defDigitSum@i#1#2@nil%
advancec@Digits by #1
ifxrelax#2relaxelseDigitSum@i#2@nilfi
pgfmathdeclarefunctionlastdigit1%
begingroup%
globalc@Digits=0
expandafterLastDigit@i#1@nil%
pgfmathparseint(thec@Digits)%
pgfmathsmugglepgfmathresultendgroup
% defLastDigit#1%
% globalc@Digits=0
% expandafterLastDigit@i#1@nil%
% pgfmathparseint(thec@Digits)
defLastDigit@i#1#2@nil%
c@Digits=#1
ifxrelax#2relaxelseLastDigit@i#2@nilfi
pgfmathdeclarefunctionintegerpower2%
begingroup%
globalc@Powers=0%
pgfmathtruncatemacropgfutil@tmpa#1%
looppgfmathtruncatemacroitestgcd(pgfutil@tmpa,#2)%0
ifnumitest>1relax%
advancec@Powers by @ne%
pgfmathtruncatemacropgfutil@tmpapgfutil@tmpa/#2%
repeat%
pgfmathparseint(thec@Powers)%
pgfmathsmugglepgfmathresultendgroup
pgfmathdeclarefunctionintegerpower21% works with large numbers
begingroup%
pgfkeys/pgf/fpu=false%
globalc@Powers=0%
PgfmathtruncatemacroFPUpgfutil@tmpa#1%
loop%
pgfmathtruncatemacropgfutil@tmpblastdigit(pgfutil@tmpa)%
pgfmathtruncatemacroitestiseven(pgfutil@tmpb)%
ifnumitest=1%
advancec@Powers by @ne%
PgfmathtruncatemacroFPUpgfutil@tmpapgfutil@tmpa/2%
repeat%
pgfmathparseint(thec@Powers)%
pgfmathsmugglepgfmathresultendgroup
pgfmathdeclarefunctionintegerpower31% works with large numbers
begingroup%
pgfkeys/pgf/fpu=false%
globalc@Powers=0%
PgfmathtruncatemacroFPUpgfutil@tmpa#1%
loop%
pgfmathtruncatemacroitestdivby3(pgfutil@tmpa)%
ifnumitest=1%
advancec@Powers by @ne%
PgfmathtruncatemacroFPUpgfutil@tmpapgfutil@tmpa/3%
repeat%
pgfmathparseint(thec@Powers)%
pgfmathsmugglepgfmathresultendgroup
pgfmathdeclarefunctionmemberQ2%
begingroup%
edefpgfutil@tmpb0%
edefpgfutil@tmpa#2%
expandafterpgfmath@member@ipgfutil@firstofone#1pgfmath@token@stop
edefpgfmathresultpgfutil@tmpb%
pgfmath@smuggleonepgfmathresult%
endgroup
defpgfmath@member@i#1%
ifxpgfmath@token@stop#1%
else
ifnum#1=pgfutil@tmparelax%
gdefpgfutil@tmpb1%
fi%
expandafterpgfmath@member@i
fi
pgfmathdeclarefunctionisevenFPU1%
begingroup%
pgfmathparseiseven(lastdigit(#1))%
pgfmathsmugglepgfmathresultendgroup
pgfmathdeclarefunctionisoddFPU1%
begingroup%
pgfmathparseisodd(lastdigit(#1))%
pgfmathsmugglepgfmathresultendgroup
pgfmathdeclarefunctiondivby31%
begingroup%
pgfmathparsememberQ(3,6,9,digitsum(digitsum(#1)))%
pgfmathsmugglepgfmathresultendgroup
pgfmathdeclarefunctiongcdFPU2%
begingroup
pgfkeys/pgf/fpu=false%
pgfmathcontinuelooptrue
PgfmathtruncatemacroFPUpgfutil@tmpa#1%
PgfmathtruncatemacroFPUpgfutil@tmpb#2%
PgfmathtruncatemacroFPUitestifthenelse(pgfutil@tmpa==0,1,0)%
ifnumitest=1relax
pgfmathcontinueloopfalse
PgfmathtruncatemacroFPUpgfutil@tmpapgfutil@tmpb%
fi%
PgfmathtruncatemacroFPUitestifthenelse(pgfutil@tmpb==0,1,0)%
ifnumitest=1relax
pgfmathcontinueloopfalse
PgfmathtruncatemacroFPUpgfutil@tmpbpgfutil@tmpa%
fi%
PgfmathtruncatemacroFPUpgfutil@tmpaabs(pgfutil@tmpa)%
PgfmathtruncatemacroFPUpgfutil@tmpbabs(pgfutil@tmpb)%
loop
ifpgfmathcontinueloop%
PgfmathtruncatemacroFPUitestifthenelse(pgfutil@tmpa==pgfutil@tmpb,1,0)%
ifnumitest=1relax
pgfmathcontinueloopfalse
else
PgfmathtruncatemacroFPUitestifthenelse(pgfutil@tmpa>pgfutil@tmpb,1,0)%
ifnumitest=1relax
PgfmathtruncatemacroFPUpgfutil@tmpapgfutil@tmpa-pgfutil@tmpb%
else
PgfmathtruncatemacroFPUpgfutil@tmpbpgfutil@tmpb-pgfutil@tmpa%
fi
fi
repeat
PgfmathtruncatemacroFPUpgfmathresultpgfutil@tmpa%
pgfmathsmugglepgfmathresultendgroup
pgfmathdeclarefunctionfactorinteger1%
begingroup% not yet done
endgroup
makeatother
newcommandPgfmathfraction[3]begingroup%
pgfmathtruncatemacromynumerator#2/gcd(#2,#3)%
pgfmathtruncatemacromydenominator#3/gcd(#2,#3)%
pgfmathsmuggle#1endgroup
begindocument
tdplotsetmaincoords7080
foreach a/b/c in 3/4/5,6/7/8,5/7/8
begintikzpicture[tdplot_main_coords,line join = round, line cap = round,
declare function=numerator(a,b,c)=pow(a,2) *pow(b,2)* pow(c,2);
denominator(a,b,c)=-pow(a,4) - pow(b,4) - pow(c,4)+%
2*pow(a,2) *pow(b,2)+2*pow(c,2) *pow(b,2)+2*pow(c,2)*pow(a,2);]
beginscope[local bounding box=elli]
PgfmathtruncatemacroFPUmynumeratornumerator(a,b,c)
PgfmathtruncatemacroFPUmydenominatordenominator(a,b,c)
PgfmathtruncatemacroFPUmygcdgcdFPU(mynumerator,mydenominator)
messagenumerator=mynumerator,denominator=mydenominator,gcd=mygcd^^J
PgfmathtruncatemacroFPUnewnumeratormynumerator/mygcd
PgfmathtruncatemacroFPUnewdenominatormydenominator/mygcd
messagenew numerator=newnumerator,new denominator=newdenominator^^J
pgfmathtruncatemacromyprenum1
pgfmathtruncatemacromypreden1
foreach Prime in 2,3,5,7,11,13,17
pgfmathtruncatemacromyintintegerpower(newnumerator,Prime)
ifnummyint>1
pgfmathtruncatemacromyint2*int(myint/2)
PgfmathtruncatemacroFPUnewnumeratornewnumerator/pow(Prime,myint)
xdefnewnumeratornewnumerator
pgfmathtruncatemacromyprenummyprenum*pow(Prime,myint/2)
xdefmyprenummyprenum
fi
pgfmathtruncatemacromyintintegerpower(newdenominator,Prime)
ifnummyint>0
pgfmathtruncatemacromyint2*int(myint/2)
PgfmathtruncatemacroFPUnewdenominatornewdenominator/pow(Prime,myint)
xdefnewdenominatornewdenominator
pgfmathtruncatemacromypredenmypreden*pow(Prime,myint/2)
xdefmypredenmypreden
fi
messagenew numerator=newnumerator, pre num=myprenum,new
denominator=newdenominator, pre den=mypreden^^J
pgfmathsetmacromyr(myprenum/mypreden)*sqrt(newnumerator/newdenominator)
coordinate (A) at (0,0,0);
coordinate (B) at (c,0,0);
coordinate (C) at ((pow(b,2) + pow(c,2) - pow(a,2))/(2*c),sqrt((a+b-c) *(a-b+c) *(-a+b+c)* (a+b+c))/(2*c),0);
coordinate (T) at (c/2, c* (a*a + b*b - c*c)/(2*sqrt((a+b-c) *(a-b+c)* (-a+b+c)* (a+b+c))),0);
foreach point/position in A/left,B/below,C/right,T/below
fill (point) circle (1.8pt);
node[position=3pt] at (point) $point$;
beginscope[canvas is xy plane at z=0]
draw[thick] (T) circle (myr);
endscope
draw (T) -- (C) node[midway,sloped,fill=white] %
$displaystyleifnummypreden=1
myprenum
else
fracmyprenummypreden
fi
ifnumnewdenominator=1
ifnumnewnumerator=1
else
cdotsqrtnewnumerator
fi
else
ifnumnewnumerator=1
cdotfrac1sqrtnewdenominator
else
cdotsqrtfracnewnumeratornewdenominator
fi
fi,$cm;
endscope
node[above] at (elli.north)$a=a,b=b,c=c$;
endtikzpicture
enddocument
answered Aug 16 at 5:49
Schrödinger's catSchrödinger's cat
3,0515 silver badges13 bronze badges
I think, your answer is not automatically.
– minhthien_2016
Aug 16 at 5:58
Dunmo. I voted for your answer. But, your code doesn't true in every cases. E.G, triangle with lenght 6, 7, 8.
– minhthien_2016
Aug 16 at 10:34
Please try with sides 3, 4, 5. It is incorrect.
– minhthien_2016
Aug 16 at 10:36
Thank you very much.
– minhthien_2016
Aug 16 at 23:05
1
You can see package xintexpr.
– minhthien_2016
Aug 17 at 4:25
|
show 3 more comments
8
There is only very limited support for fraction detection and so on in pgf, and as soon as square roots are involved I think you do need to do some of the things by hand. (To be fair, computer algebra systems are also not great at detecting such expressions, but if you use those to parse the expressions then you can get exact result. Yet LaTeX is not such a computer algebra system.) You can use the keys
pgfkeys/pgf/number format/.cd,frac, frac denom=3,frac whole=false
to obtain
documentclass[border = 1mm]standalone
usepackagetikz
usepackagetikz-3dplot
usetikzlibraryintersections,calc,backgrounds,fpu
newcommandPgfmathsetmacroFPU[2]begingroup%
pgfkeys/pgf/fpu,/pgf/fpu/output format=fixed%
pgfmathsetmacro#1#2%
pgfmathsmuggle#1endgroup
begindocument
tdplotsetmaincoords7080
begintikzpicture[tdplot_main_coords,line join = round, line cap = round]
pgfmathsetmacroa5
pgfmathsetmacrob7
pgfmathsetmacroc8
PgfmathsetmacroFPUmyrsqrt(-
pow(a,2) *pow(b,2)* pow(c,2)/ (pow(a,4) + pow(b,4) + pow(c,4)- 2
*pow(a,2) *pow(b,2) - 2*pow(c,2) *pow(b,2)-2*pow(c,2) *pow(a,2) ))
coordinate (A) at (0,0,0);
coordinate (B) at (c,0,0);
coordinate (C) at ((pow(b,2) + pow(c,2) - pow(a,2))/(2*c),sqrt((a+b-c) *(a-b+c) *(-a+b+c)* (a+b+c))/(2*c),0);
coordinate (T) at (c/2, c* (a*a + b*b - c*c)/(2*sqrt((a+b-c) *(a-b+c)* (-a+b+c)* (a+b+c))),0);
foreach point/position in A/left,B/below,C/right,T/below
fill (point) circle (1.8pt);
node[position=3pt] at (point) $point$;
beginscope[canvas is xy plane at z=0]
draw[thick] (T) circle (myr);
endscope
draw (T) -- (C) node[midway,sloped,fill=white] %
pgfmathparsemyr/sqrt(3)%
pgfkeys/pgf/number format/.cd,frac, frac denom=3,frac whole=false%
$pgfmathprintnumberpgfmathresultcdotsqrt3,$cm;
endtikzpicture
enddocument
Of course, one can do better than that but to the best of my knowledge the routines for doing the required integer arithmetic are not yet implemented in pgf (and there is a slight chance that there is no real package for those). The main obstacle is that gcd, which is very useful to cancel common factors in fractions, does not yet work with fpu. On the other hand, you need fpu here because the numbers are so large. So I added variant of gcd (called gcdFPU) and a number of other routines such as integerpower which allows one to determine the power of a factor in an integer. For instance, integerpower(12,2) yields 2 since 12=2^2 times something that is not divisible by 2. This can be used to pull squares out of the square root.
documentclass[tikz,border=1mm]standalone
usepackagetikz-3dplot
usetikzlibraryfpu
newcounterifactor
newcommandPgfmathsetmacroFPU[2]begingroup%
pgfkeys/pgf/fpu,/pgf/fpu/output format=fixed%
pgfmathsetmacro#1#2%
pgfmathsmuggle#1endgroup
newcommandPgfmathtruncatemacroFPU[2]begingroup%
pgfkeys/pgf/fpu,/pgf/fpu/output format=fixed%
pgfmathtruncatemacro#1round(#2)%
pgfmathsmuggle#1endgroup
% the following functions are based on
% * https://tex.stackexchange.com/a/177109 (digitcount,digitsum,lastdigit)
% * https://tex.stackexchange.com/a/501895 (memberQ)
% or new in the sense that they were developed on the basis of the existing
% pgf functions
makeatletter
newcountc@Digits
newcountc@Powers
pgfmathdeclarefunctiondigitcount1%
begingroup%
globalc@Digits=0
expandafterDigitCount@i#1@nil%
pgfmathparseint(thec@Digits)%
pgfmathsmugglepgfmathresultendgroup
% defGroupDigits#1%
% globalc@Digits=0
% expandafterDigitCount@i#1@nil%
% pgfmathparseint(thec@Digits)
defDigitCount@i#1#2@nil%
advancec@Digits by @ne
ifxrelax#2relaxelseDigitCount@i#2@nilfi
pgfmathdeclarefunctiondigitsum1%
begingroup%
globalc@Digits=0
expandafterDigitSum@i#1@nil%
pgfmathparseint(thec@Digits)%
pgfmathsmugglepgfmathresultendgroup
% defDigitSum#1%
% globalc@Digits=0
% expandafterDigitSum@i#1@nil%
% pgfmathparseint(thec@Digits)
defDigitSum@i#1#2@nil%
advancec@Digits by #1
ifxrelax#2relaxelseDigitSum@i#2@nilfi
pgfmathdeclarefunctionlastdigit1%
begingroup%
globalc@Digits=0
expandafterLastDigit@i#1@nil%
pgfmathparseint(thec@Digits)%
pgfmathsmugglepgfmathresultendgroup
% defLastDigit#1%
% globalc@Digits=0
% expandafterLastDigit@i#1@nil%
% pgfmathparseint(thec@Digits)
defLastDigit@i#1#2@nil%
c@Digits=#1
ifxrelax#2relaxelseLastDigit@i#2@nilfi
pgfmathdeclarefunctionintegerpower2%
begingroup%
globalc@Powers=0%
pgfmathtruncatemacropgfutil@tmpa#1%
looppgfmathtruncatemacroitestgcd(pgfutil@tmpa,#2)%0
ifnumitest>1relax%
advancec@Powers by @ne%
pgfmathtruncatemacropgfutil@tmpapgfutil@tmpa/#2%
repeat%
pgfmathparseint(thec@Powers)%
pgfmathsmugglepgfmathresultendgroup
pgfmathdeclarefunctionintegerpower21% works with large numbers
begingroup%
pgfkeys/pgf/fpu=false%
globalc@Powers=0%
PgfmathtruncatemacroFPUpgfutil@tmpa#1%
loop%
pgfmathtruncatemacropgfutil@tmpblastdigit(pgfutil@tmpa)%
pgfmathtruncatemacroitestiseven(pgfutil@tmpb)%
ifnumitest=1%
advancec@Powers by @ne%
PgfmathtruncatemacroFPUpgfutil@tmpapgfutil@tmpa/2%
repeat%
pgfmathparseint(thec@Powers)%
pgfmathsmugglepgfmathresultendgroup
pgfmathdeclarefunctionintegerpower31% works with large numbers
begingroup%
pgfkeys/pgf/fpu=false%
globalc@Powers=0%
PgfmathtruncatemacroFPUpgfutil@tmpa#1%
loop%
pgfmathtruncatemacroitestdivby3(pgfutil@tmpa)%
ifnumitest=1%
advancec@Powers by @ne%
PgfmathtruncatemacroFPUpgfutil@tmpapgfutil@tmpa/3%
repeat%
pgfmathparseint(thec@Powers)%
pgfmathsmugglepgfmathresultendgroup
pgfmathdeclarefunctionmemberQ2%
begingroup%
edefpgfutil@tmpb0%
edefpgfutil@tmpa#2%
expandafterpgfmath@member@ipgfutil@firstofone#1pgfmath@token@stop
edefpgfmathresultpgfutil@tmpb%
pgfmath@smuggleonepgfmathresult%
endgroup
defpgfmath@member@i#1%
ifxpgfmath@token@stop#1%
else
ifnum#1=pgfutil@tmparelax%
gdefpgfutil@tmpb1%
fi%
expandafterpgfmath@member@i
fi
pgfmathdeclarefunctionisevenFPU1%
begingroup%
pgfmathparseiseven(lastdigit(#1))%
pgfmathsmugglepgfmathresultendgroup
pgfmathdeclarefunctionisoddFPU1%
begingroup%
pgfmathparseisodd(lastdigit(#1))%
pgfmathsmugglepgfmathresultendgroup
pgfmathdeclarefunctiondivby31%
begingroup%
pgfmathparsememberQ(3,6,9,digitsum(digitsum(#1)))%
pgfmathsmugglepgfmathresultendgroup
pgfmathdeclarefunctiongcdFPU2%
begingroup
pgfkeys/pgf/fpu=false%
pgfmathcontinuelooptrue
PgfmathtruncatemacroFPUpgfutil@tmpa#1%
PgfmathtruncatemacroFPUpgfutil@tmpb#2%
PgfmathtruncatemacroFPUitestifthenelse(pgfutil@tmpa==0,1,0)%
ifnumitest=1relax
pgfmathcontinueloopfalse
PgfmathtruncatemacroFPUpgfutil@tmpapgfutil@tmpb%
fi%
PgfmathtruncatemacroFPUitestifthenelse(pgfutil@tmpb==0,1,0)%
ifnumitest=1relax
pgfmathcontinueloopfalse
PgfmathtruncatemacroFPUpgfutil@tmpbpgfutil@tmpa%
fi%
PgfmathtruncatemacroFPUpgfutil@tmpaabs(pgfutil@tmpa)%
PgfmathtruncatemacroFPUpgfutil@tmpbabs(pgfutil@tmpb)%
loop
ifpgfmathcontinueloop%
PgfmathtruncatemacroFPUitestifthenelse(pgfutil@tmpa==pgfutil@tmpb,1,0)%
ifnumitest=1relax
pgfmathcontinueloopfalse
else
PgfmathtruncatemacroFPUitestifthenelse(pgfutil@tmpa>pgfutil@tmpb,1,0)%
ifnumitest=1relax
PgfmathtruncatemacroFPUpgfutil@tmpapgfutil@tmpa-pgfutil@tmpb%
else
PgfmathtruncatemacroFPUpgfutil@tmpbpgfutil@tmpb-pgfutil@tmpa%
fi
fi
repeat
PgfmathtruncatemacroFPUpgfmathresultpgfutil@tmpa%
pgfmathsmugglepgfmathresultendgroup
pgfmathdeclarefunctionfactorinteger1%
begingroup% not yet done
endgroup
makeatother
newcommandPgfmathfraction[3]begingroup%
pgfmathtruncatemacromynumerator#2/gcd(#2,#3)%
pgfmathtruncatemacromydenominator#3/gcd(#2,#3)%
pgfmathsmuggle#1endgroup
begindocument
tdplotsetmaincoords7080
foreach a/b/c in 3/4/5,6/7/8,5/7/8
begintikzpicture[tdplot_main_coords,line join = round, line cap = round,
declare function=numerator(a,b,c)=pow(a,2) *pow(b,2)* pow(c,2);
denominator(a,b,c)=-pow(a,4) - pow(b,4) - pow(c,4)+%
2*pow(a,2) *pow(b,2)+2*pow(c,2) *pow(b,2)+2*pow(c,2)*pow(a,2);]
beginscope[local bounding box=elli]
PgfmathtruncatemacroFPUmynumeratornumerator(a,b,c)
PgfmathtruncatemacroFPUmydenominatordenominator(a,b,c)
PgfmathtruncatemacroFPUmygcdgcdFPU(mynumerator,mydenominator)
messagenumerator=mynumerator,denominator=mydenominator,gcd=mygcd^^J
PgfmathtruncatemacroFPUnewnumeratormynumerator/mygcd
PgfmathtruncatemacroFPUnewdenominatormydenominator/mygcd
messagenew numerator=newnumerator,new denominator=newdenominator^^J
pgfmathtruncatemacromyprenum1
pgfmathtruncatemacromypreden1
foreach Prime in 2,3,5,7,11,13,17
pgfmathtruncatemacromyintintegerpower(newnumerator,Prime)
ifnummyint>1
pgfmathtruncatemacromyint2*int(myint/2)
PgfmathtruncatemacroFPUnewnumeratornewnumerator/pow(Prime,myint)
xdefnewnumeratornewnumerator
pgfmathtruncatemacromyprenummyprenum*pow(Prime,myint/2)
xdefmyprenummyprenum
fi
pgfmathtruncatemacromyintintegerpower(newdenominator,Prime)
ifnummyint>0
pgfmathtruncatemacromyint2*int(myint/2)
PgfmathtruncatemacroFPUnewdenominatornewdenominator/pow(Prime,myint)
xdefnewdenominatornewdenominator
pgfmathtruncatemacromypredenmypreden*pow(Prime,myint/2)
xdefmypredenmypreden
fi
messagenew numerator=newnumerator, pre num=myprenum,new
denominator=newdenominator, pre den=mypreden^^J
pgfmathsetmacromyr(myprenum/mypreden)*sqrt(newnumerator/newdenominator)
coordinate (A) at (0,0,0);
coordinate (B) at (c,0,0);
coordinate (C) at ((pow(b,2) + pow(c,2) - pow(a,2))/(2*c),sqrt((a+b-c) *(a-b+c) *(-a+b+c)* (a+b+c))/(2*c),0);
coordinate (T) at (c/2, c* (a*a + b*b - c*c)/(2*sqrt((a+b-c) *(a-b+c)* (-a+b+c)* (a+b+c))),0);
foreach point/position in A/left,B/below,C/right,T/below
fill (point) circle (1.8pt);
node[position=3pt] at (point) $point$;
beginscope[canvas is xy plane at z=0]
draw[thick] (T) circle (myr);
endscope
draw (T) -- (C) node[midway,sloped,fill=white] %
$displaystyleifnummypreden=1
myprenum
else
fracmyprenummypreden
fi
ifnumnewdenominator=1
ifnumnewnumerator=1
else
cdotsqrtnewnumerator
fi
else
ifnumnewnumerator=1
cdotfrac1sqrtnewdenominator
else
cdotsqrtfracnewnumeratornewdenominator
fi
fi,$cm;
endscope
node[above] at (elli.north)$a=a,b=b,c=c$;
endtikzpicture
enddocument
answered Aug 16 at 5:49
Schrödinger's catSchrödinger's cat
3,0515 silver badges13 bronze badges
I think, your answer is not automatically.
– minhthien_2016
Aug 16 at 5:58
Dunmo. I voted for your answer. But, your code doesn't true in every cases. E.G, triangle with lenght 6, 7, 8.
– minhthien_2016
Aug 16 at 10:34
Please try with sides 3, 4, 5. It is incorrect.
– minhthien_2016
Aug 16 at 10:36
Thank you very much.
– minhthien_2016
Aug 16 at 23:05
1
You can see package xintexpr.
– minhthien_2016
Aug 17 at 4:25
|
show 3 more comments
8
8
8
There is only very limited support for fraction detection and so on in pgf, and as soon as square roots are involved I think you do need to do some of the things by hand. (To be fair, computer algebra systems are also not great at detecting such expressions, but if you use those to parse the expressions then you can get exact result. Yet LaTeX is not such a computer algebra system.) You can use the keys
pgfkeys/pgf/number format/.cd,frac, frac denom=3,frac whole=false
to obtain
documentclass[border = 1mm]standalone
usepackagetikz
usepackagetikz-3dplot
usetikzlibraryintersections,calc,backgrounds,fpu
newcommandPgfmathsetmacroFPU[2]begingroup%
pgfkeys/pgf/fpu,/pgf/fpu/output format=fixed%
pgfmathsetmacro#1#2%
pgfmathsmuggle#1endgroup
begindocument
tdplotsetmaincoords7080
begintikzpicture[tdplot_main_coords,line join = round, line cap = round]
pgfmathsetmacroa5
pgfmathsetmacrob7
pgfmathsetmacroc8
PgfmathsetmacroFPUmyrsqrt(-
pow(a,2) *pow(b,2)* pow(c,2)/ (pow(a,4) + pow(b,4) + pow(c,4)- 2
*pow(a,2) *pow(b,2) - 2*pow(c,2) *pow(b,2)-2*pow(c,2) *pow(a,2) ))
coordinate (A) at (0,0,0);
coordinate (B) at (c,0,0);
coordinate (C) at ((pow(b,2) + pow(c,2) - pow(a,2))/(2*c),sqrt((a+b-c) *(a-b+c) *(-a+b+c)* (a+b+c))/(2*c),0);
coordinate (T) at (c/2, c* (a*a + b*b - c*c)/(2*sqrt((a+b-c) *(a-b+c)* (-a+b+c)* (a+b+c))),0);
foreach point/position in A/left,B/below,C/right,T/below
fill (point) circle (1.8pt);
node[position=3pt] at (point) $point$;
beginscope[canvas is xy plane at z=0]
draw[thick] (T) circle (myr);
endscope
draw (T) -- (C) node[midway,sloped,fill=white] %
pgfmathparsemyr/sqrt(3)%
pgfkeys/pgf/number format/.cd,frac, frac denom=3,frac whole=false%
$pgfmathprintnumberpgfmathresultcdotsqrt3,$cm;
endtikzpicture
enddocument
Of course, one can do better than that but to the best of my knowledge the routines for doing the required integer arithmetic are not yet implemented in pgf (and there is a slight chance that there is no real package for those). The main obstacle is that gcd, which is very useful to cancel common factors in fractions, does not yet work with fpu. On the other hand, you need fpu here because the numbers are so large. So I added variant of gcd (called gcdFPU) and a number of other routines such as integerpower which allows one to determine the power of a factor in an integer. For instance, integerpower(12,2) yields 2 since 12=2^2 times something that is not divisible by 2. This can be used to pull squares out of the square root.
documentclass[tikz,border=1mm]standalone
usepackagetikz-3dplot
usetikzlibraryfpu
newcounterifactor
newcommandPgfmathsetmacroFPU[2]begingroup%
pgfkeys/pgf/fpu,/pgf/fpu/output format=fixed%
pgfmathsetmacro#1#2%
pgfmathsmuggle#1endgroup
newcommandPgfmathtruncatemacroFPU[2]begingroup%
pgfkeys/pgf/fpu,/pgf/fpu/output format=fixed%
pgfmathtruncatemacro#1round(#2)%
pgfmathsmuggle#1endgroup
% the following functions are based on
% * https://tex.stackexchange.com/a/177109 (digitcount,digitsum,lastdigit)
% * https://tex.stackexchange.com/a/501895 (memberQ)
% or new in the sense that they were developed on the basis of the existing
% pgf functions
makeatletter
newcountc@Digits
newcountc@Powers
pgfmathdeclarefunctiondigitcount1%
begingroup%
globalc@Digits=0
expandafterDigitCount@i#1@nil%
pgfmathparseint(thec@Digits)%
pgfmathsmugglepgfmathresultendgroup
% defGroupDigits#1%
% globalc@Digits=0
% expandafterDigitCount@i#1@nil%
% pgfmathparseint(thec@Digits)
defDigitCount@i#1#2@nil%
advancec@Digits by @ne
ifxrelax#2relaxelseDigitCount@i#2@nilfi
pgfmathdeclarefunctiondigitsum1%
begingroup%
globalc@Digits=0
expandafterDigitSum@i#1@nil%
pgfmathparseint(thec@Digits)%
pgfmathsmugglepgfmathresultendgroup
% defDigitSum#1%
% globalc@Digits=0
% expandafterDigitSum@i#1@nil%
% pgfmathparseint(thec@Digits)
defDigitSum@i#1#2@nil%
advancec@Digits by #1
ifxrelax#2relaxelseDigitSum@i#2@nilfi
pgfmathdeclarefunctionlastdigit1%
begingroup%
globalc@Digits=0
expandafterLastDigit@i#1@nil%
pgfmathparseint(thec@Digits)%
pgfmathsmugglepgfmathresultendgroup
% defLastDigit#1%
% globalc@Digits=0
% expandafterLastDigit@i#1@nil%
% pgfmathparseint(thec@Digits)
defLastDigit@i#1#2@nil%
c@Digits=#1
ifxrelax#2relaxelseLastDigit@i#2@nilfi
pgfmathdeclarefunctionintegerpower2%
begingroup%
globalc@Powers=0%
pgfmathtruncatemacropgfutil@tmpa#1%
looppgfmathtruncatemacroitestgcd(pgfutil@tmpa,#2)%0
ifnumitest>1relax%
advancec@Powers by @ne%
pgfmathtruncatemacropgfutil@tmpapgfutil@tmpa/#2%
repeat%
pgfmathparseint(thec@Powers)%
pgfmathsmugglepgfmathresultendgroup
pgfmathdeclarefunctionintegerpower21% works with large numbers
begingroup%
pgfkeys/pgf/fpu=false%
globalc@Powers=0%
PgfmathtruncatemacroFPUpgfutil@tmpa#1%
loop%
pgfmathtruncatemacropgfutil@tmpblastdigit(pgfutil@tmpa)%
pgfmathtruncatemacroitestiseven(pgfutil@tmpb)%
ifnumitest=1%
advancec@Powers by @ne%
PgfmathtruncatemacroFPUpgfutil@tmpapgfutil@tmpa/2%
repeat%
pgfmathparseint(thec@Powers)%
pgfmathsmugglepgfmathresultendgroup
pgfmathdeclarefunctionintegerpower31% works with large numbers
begingroup%
pgfkeys/pgf/fpu=false%
globalc@Powers=0%
PgfmathtruncatemacroFPUpgfutil@tmpa#1%
loop%
pgfmathtruncatemacroitestdivby3(pgfutil@tmpa)%
ifnumitest=1%
advancec@Powers by @ne%
PgfmathtruncatemacroFPUpgfutil@tmpapgfutil@tmpa/3%
repeat%
pgfmathparseint(thec@Powers)%
pgfmathsmugglepgfmathresultendgroup
pgfmathdeclarefunctionmemberQ2%
begingroup%
edefpgfutil@tmpb0%
edefpgfutil@tmpa#2%
expandafterpgfmath@member@ipgfutil@firstofone#1pgfmath@token@stop
edefpgfmathresultpgfutil@tmpb%
pgfmath@smuggleonepgfmathresult%
endgroup
defpgfmath@member@i#1%
ifxpgfmath@token@stop#1%
else
ifnum#1=pgfutil@tmparelax%
gdefpgfutil@tmpb1%
fi%
expandafterpgfmath@member@i
fi
pgfmathdeclarefunctionisevenFPU1%
begingroup%
pgfmathparseiseven(lastdigit(#1))%
pgfmathsmugglepgfmathresultendgroup
pgfmathdeclarefunctionisoddFPU1%
begingroup%
pgfmathparseisodd(lastdigit(#1))%
pgfmathsmugglepgfmathresultendgroup
pgfmathdeclarefunctiondivby31%
begingroup%
pgfmathparsememberQ(3,6,9,digitsum(digitsum(#1)))%
pgfmathsmugglepgfmathresultendgroup
pgfmathdeclarefunctiongcdFPU2%
begingroup
pgfkeys/pgf/fpu=false%
pgfmathcontinuelooptrue
PgfmathtruncatemacroFPUpgfutil@tmpa#1%
PgfmathtruncatemacroFPUpgfutil@tmpb#2%
PgfmathtruncatemacroFPUitestifthenelse(pgfutil@tmpa==0,1,0)%
ifnumitest=1relax
pgfmathcontinueloopfalse
PgfmathtruncatemacroFPUpgfutil@tmpapgfutil@tmpb%
fi%
PgfmathtruncatemacroFPUitestifthenelse(pgfutil@tmpb==0,1,0)%
ifnumitest=1relax
pgfmathcontinueloopfalse
PgfmathtruncatemacroFPUpgfutil@tmpbpgfutil@tmpa%
fi%
PgfmathtruncatemacroFPUpgfutil@tmpaabs(pgfutil@tmpa)%
PgfmathtruncatemacroFPUpgfutil@tmpbabs(pgfutil@tmpb)%
loop
ifpgfmathcontinueloop%
PgfmathtruncatemacroFPUitestifthenelse(pgfutil@tmpa==pgfutil@tmpb,1,0)%
ifnumitest=1relax
pgfmathcontinueloopfalse
else
PgfmathtruncatemacroFPUitestifthenelse(pgfutil@tmpa>pgfutil@tmpb,1,0)%
ifnumitest=1relax
PgfmathtruncatemacroFPUpgfutil@tmpapgfutil@tmpa-pgfutil@tmpb%
else
PgfmathtruncatemacroFPUpgfutil@tmpbpgfutil@tmpb-pgfutil@tmpa%
fi
fi
repeat
PgfmathtruncatemacroFPUpgfmathresultpgfutil@tmpa%
pgfmathsmugglepgfmathresultendgroup
pgfmathdeclarefunctionfactorinteger1%
begingroup% not yet done
endgroup
makeatother
newcommandPgfmathfraction[3]begingroup%
pgfmathtruncatemacromynumerator#2/gcd(#2,#3)%
pgfmathtruncatemacromydenominator#3/gcd(#2,#3)%
pgfmathsmuggle#1endgroup
begindocument
tdplotsetmaincoords7080
foreach a/b/c in 3/4/5,6/7/8,5/7/8
begintikzpicture[tdplot_main_coords,line join = round, line cap = round,
declare function=numerator(a,b,c)=pow(a,2) *pow(b,2)* pow(c,2);
denominator(a,b,c)=-pow(a,4) - pow(b,4) - pow(c,4)+%
2*pow(a,2) *pow(b,2)+2*pow(c,2) *pow(b,2)+2*pow(c,2)*pow(a,2);]
beginscope[local bounding box=elli]
PgfmathtruncatemacroFPUmynumeratornumerator(a,b,c)
PgfmathtruncatemacroFPUmydenominatordenominator(a,b,c)
PgfmathtruncatemacroFPUmygcdgcdFPU(mynumerator,mydenominator)
messagenumerator=mynumerator,denominator=mydenominator,gcd=mygcd^^J
PgfmathtruncatemacroFPUnewnumeratormynumerator/mygcd
PgfmathtruncatemacroFPUnewdenominatormydenominator/mygcd
messagenew numerator=newnumerator,new denominator=newdenominator^^J
pgfmathtruncatemacromyprenum1
pgfmathtruncatemacromypreden1
foreach Prime in 2,3,5,7,11,13,17
pgfmathtruncatemacromyintintegerpower(newnumerator,Prime)
ifnummyint>1
pgfmathtruncatemacromyint2*int(myint/2)
PgfmathtruncatemacroFPUnewnumeratornewnumerator/pow(Prime,myint)
xdefnewnumeratornewnumerator
pgfmathtruncatemacromyprenummyprenum*pow(Prime,myint/2)
xdefmyprenummyprenum
fi
pgfmathtruncatemacromyintintegerpower(newdenominator,Prime)
ifnummyint>0
pgfmathtruncatemacromyint2*int(myint/2)
PgfmathtruncatemacroFPUnewdenominatornewdenominator/pow(Prime,myint)
xdefnewdenominatornewdenominator
pgfmathtruncatemacromypredenmypreden*pow(Prime,myint/2)
xdefmypredenmypreden
fi
messagenew numerator=newnumerator, pre num=myprenum,new
denominator=newdenominator, pre den=mypreden^^J
pgfmathsetmacromyr(myprenum/mypreden)*sqrt(newnumerator/newdenominator)
coordinate (A) at (0,0,0);
coordinate (B) at (c,0,0);
coordinate (C) at ((pow(b,2) + pow(c,2) - pow(a,2))/(2*c),sqrt((a+b-c) *(a-b+c) *(-a+b+c)* (a+b+c))/(2*c),0);
coordinate (T) at (c/2, c* (a*a + b*b - c*c)/(2*sqrt((a+b-c) *(a-b+c)* (-a+b+c)* (a+b+c))),0);
foreach point/position in A/left,B/below,C/right,T/below
fill (point) circle (1.8pt);
node[position=3pt] at (point) $point$;
beginscope[canvas is xy plane at z=0]
draw[thick] (T) circle (myr);
endscope
draw (T) -- (C) node[midway,sloped,fill=white] %
$displaystyleifnummypreden=1
myprenum
else
fracmyprenummypreden
fi
ifnumnewdenominator=1
ifnumnewnumerator=1
else
cdotsqrtnewnumerator
fi
else
ifnumnewnumerator=1
cdotfrac1sqrtnewdenominator
else
cdotsqrtfracnewnumeratornewdenominator
fi
fi,$cm;
endscope
node[above] at (elli.north)$a=a,b=b,c=c$;
endtikzpicture
enddocument
answered Aug 16 at 5:49
Schrödinger's catSchrödinger's cat
3,0515 silver badges13 bronze badges
There is only very limited support for fraction detection and so on in pgf, and as soon as square roots are involved I think you do need to do some of the things by hand. (To be fair, computer algebra systems are also not great at detecting such expressions, but if you use those to parse the expressions then you can get exact result. Yet LaTeX is not such a computer algebra system.) You can use the keys
pgfkeys/pgf/number format/.cd,frac, frac denom=3,frac whole=false
to obtain
documentclass[border = 1mm]standalone
usepackagetikz
usepackagetikz-3dplot
usetikzlibraryintersections,calc,backgrounds,fpu
newcommandPgfmathsetmacroFPU[2]begingroup%
pgfkeys/pgf/fpu,/pgf/fpu/output format=fixed%
pgfmathsetmacro#1#2%
pgfmathsmuggle#1endgroup
begindocument
tdplotsetmaincoords7080
begintikzpicture[tdplot_main_coords,line join = round, line cap = round]
pgfmathsetmacroa5
pgfmathsetmacrob7
pgfmathsetmacroc8
PgfmathsetmacroFPUmyrsqrt(-
pow(a,2) *pow(b,2)* pow(c,2)/ (pow(a,4) + pow(b,4) + pow(c,4)- 2
*pow(a,2) *pow(b,2) - 2*pow(c,2) *pow(b,2)-2*pow(c,2) *pow(a,2) ))
coordinate (A) at (0,0,0);
coordinate (B) at (c,0,0);
coordinate (C) at ((pow(b,2) + pow(c,2) - pow(a,2))/(2*c),sqrt((a+b-c) *(a-b+c) *(-a+b+c)* (a+b+c))/(2*c),0);
coordinate (T) at (c/2, c* (a*a + b*b - c*c)/(2*sqrt((a+b-c) *(a-b+c)* (-a+b+c)* (a+b+c))),0);
foreach point/position in A/left,B/below,C/right,T/below
fill (point) circle (1.8pt);
node[position=3pt] at (point) $point$;
beginscope[canvas is xy plane at z=0]
draw[thick] (T) circle (myr);
endscope
draw (T) -- (C) node[midway,sloped,fill=white] %
pgfmathparsemyr/sqrt(3)%
pgfkeys/pgf/number format/.cd,frac, frac denom=3,frac whole=false%
$pgfmathprintnumberpgfmathresultcdotsqrt3,$cm;
endtikzpicture
enddocument
Of course, one can do better than that but to the best of my knowledge the routines for doing the required integer arithmetic are not yet implemented in pgf (and there is a slight chance that there is no real package for those). The main obstacle is that gcd, which is very useful to cancel common factors in fractions, does not yet work with fpu. On the other hand, you need fpu here because the numbers are so large. So I added variant of gcd (called gcdFPU) and a number of other routines such as integerpower which allows one to determine the power of a factor in an integer. For instance, integerpower(12,2) yields 2 since 12=2^2 times something that is not divisible by 2. This can be used to pull squares out of the square root.
documentclass[tikz,border=1mm]standalone
usepackagetikz-3dplot
usetikzlibraryfpu
newcounterifactor
newcommandPgfmathsetmacroFPU[2]begingroup%
pgfkeys/pgf/fpu,/pgf/fpu/output format=fixed%
pgfmathsetmacro#1#2%
pgfmathsmuggle#1endgroup
newcommandPgfmathtruncatemacroFPU[2]begingroup%
pgfkeys/pgf/fpu,/pgf/fpu/output format=fixed%
pgfmathtruncatemacro#1round(#2)%
pgfmathsmuggle#1endgroup
% the following functions are based on
% * https://tex.stackexchange.com/a/177109 (digitcount,digitsum,lastdigit)
% * https://tex.stackexchange.com/a/501895 (memberQ)
% or new in the sense that they were developed on the basis of the existing
% pgf functions
makeatletter
newcountc@Digits
newcountc@Powers
pgfmathdeclarefunctiondigitcount1%
begingroup%
globalc@Digits=0
expandafterDigitCount@i#1@nil%
pgfmathparseint(thec@Digits)%
pgfmathsmugglepgfmathresultendgroup
% defGroupDigits#1%
% globalc@Digits=0
% expandafterDigitCount@i#1@nil%
% pgfmathparseint(thec@Digits)
defDigitCount@i#1#2@nil%
advancec@Digits by @ne
ifxrelax#2relaxelseDigitCount@i#2@nilfi
pgfmathdeclarefunctiondigitsum1%
begingroup%
globalc@Digits=0
expandafterDigitSum@i#1@nil%
pgfmathparseint(thec@Digits)%
pgfmathsmugglepgfmathresultendgroup
% defDigitSum#1%
% globalc@Digits=0
% expandafterDigitSum@i#1@nil%
% pgfmathparseint(thec@Digits)
defDigitSum@i#1#2@nil%
advancec@Digits by #1
ifxrelax#2relaxelseDigitSum@i#2@nilfi
pgfmathdeclarefunctionlastdigit1%
begingroup%
globalc@Digits=0
expandafterLastDigit@i#1@nil%
pgfmathparseint(thec@Digits)%
pgfmathsmugglepgfmathresultendgroup
% defLastDigit#1%
% globalc@Digits=0
% expandafterLastDigit@i#1@nil%
% pgfmathparseint(thec@Digits)
defLastDigit@i#1#2@nil%
c@Digits=#1
ifxrelax#2relaxelseLastDigit@i#2@nilfi
pgfmathdeclarefunctionintegerpower2%
begingroup%
globalc@Powers=0%
pgfmathtruncatemacropgfutil@tmpa#1%
looppgfmathtruncatemacroitestgcd(pgfutil@tmpa,#2)%0
ifnumitest>1relax%
advancec@Powers by @ne%
pgfmathtruncatemacropgfutil@tmpapgfutil@tmpa/#2%
repeat%
pgfmathparseint(thec@Powers)%
pgfmathsmugglepgfmathresultendgroup
pgfmathdeclarefunctionintegerpower21% works with large numbers
begingroup%
pgfkeys/pgf/fpu=false%
globalc@Powers=0%
PgfmathtruncatemacroFPUpgfutil@tmpa#1%
loop%
pgfmathtruncatemacropgfutil@tmpblastdigit(pgfutil@tmpa)%
pgfmathtruncatemacroitestiseven(pgfutil@tmpb)%
ifnumitest=1%
advancec@Powers by @ne%
PgfmathtruncatemacroFPUpgfutil@tmpapgfutil@tmpa/2%
repeat%
pgfmathparseint(thec@Powers)%
pgfmathsmugglepgfmathresultendgroup
pgfmathdeclarefunctionintegerpower31% works with large numbers
begingroup%
pgfkeys/pgf/fpu=false%
globalc@Powers=0%
PgfmathtruncatemacroFPUpgfutil@tmpa#1%
loop%
pgfmathtruncatemacroitestdivby3(pgfutil@tmpa)%
ifnumitest=1%
advancec@Powers by @ne%
PgfmathtruncatemacroFPUpgfutil@tmpapgfutil@tmpa/3%
repeat%
pgfmathparseint(thec@Powers)%
pgfmathsmugglepgfmathresultendgroup
pgfmathdeclarefunctionmemberQ2%
begingroup%
edefpgfutil@tmpb0%
edefpgfutil@tmpa#2%
expandafterpgfmath@member@ipgfutil@firstofone#1pgfmath@token@stop
edefpgfmathresultpgfutil@tmpb%
pgfmath@smuggleonepgfmathresult%
endgroup
defpgfmath@member@i#1%
ifxpgfmath@token@stop#1%
else
ifnum#1=pgfutil@tmparelax%
gdefpgfutil@tmpb1%
fi%
expandafterpgfmath@member@i
fi
pgfmathdeclarefunctionisevenFPU1%
begingroup%
pgfmathparseiseven(lastdigit(#1))%
pgfmathsmugglepgfmathresultendgroup
pgfmathdeclarefunctionisoddFPU1%
begingroup%
pgfmathparseisodd(lastdigit(#1))%
pgfmathsmugglepgfmathresultendgroup
pgfmathdeclarefunctiondivby31%
begingroup%
pgfmathparsememberQ(3,6,9,digitsum(digitsum(#1)))%
pgfmathsmugglepgfmathresultendgroup
pgfmathdeclarefunctiongcdFPU2%
begingroup
pgfkeys/pgf/fpu=false%
pgfmathcontinuelooptrue
PgfmathtruncatemacroFPUpgfutil@tmpa#1%
PgfmathtruncatemacroFPUpgfutil@tmpb#2%
PgfmathtruncatemacroFPUitestifthenelse(pgfutil@tmpa==0,1,0)%
ifnumitest=1relax
pgfmathcontinueloopfalse
PgfmathtruncatemacroFPUpgfutil@tmpapgfutil@tmpb%
fi%
PgfmathtruncatemacroFPUitestifthenelse(pgfutil@tmpb==0,1,0)%
ifnumitest=1relax
pgfmathcontinueloopfalse
PgfmathtruncatemacroFPUpgfutil@tmpbpgfutil@tmpa%
fi%
PgfmathtruncatemacroFPUpgfutil@tmpaabs(pgfutil@tmpa)%
PgfmathtruncatemacroFPUpgfutil@tmpbabs(pgfutil@tmpb)%
loop
ifpgfmathcontinueloop%
PgfmathtruncatemacroFPUitestifthenelse(pgfutil@tmpa==pgfutil@tmpb,1,0)%
ifnumitest=1relax
pgfmathcontinueloopfalse
else
PgfmathtruncatemacroFPUitestifthenelse(pgfutil@tmpa>pgfutil@tmpb,1,0)%
ifnumitest=1relax
PgfmathtruncatemacroFPUpgfutil@tmpapgfutil@tmpa-pgfutil@tmpb%
else
PgfmathtruncatemacroFPUpgfutil@tmpbpgfutil@tmpb-pgfutil@tmpa%
fi
fi
repeat
PgfmathtruncatemacroFPUpgfmathresultpgfutil@tmpa%
pgfmathsmugglepgfmathresultendgroup
pgfmathdeclarefunctionfactorinteger1%
begingroup% not yet done
endgroup
makeatother
newcommandPgfmathfraction[3]begingroup%
pgfmathtruncatemacromynumerator#2/gcd(#2,#3)%
pgfmathtruncatemacromydenominator#3/gcd(#2,#3)%
pgfmathsmuggle#1endgroup
begindocument
tdplotsetmaincoords7080
foreach a/b/c in 3/4/5,6/7/8,5/7/8
begintikzpicture[tdplot_main_coords,line join = round, line cap = round,
declare function=numerator(a,b,c)=pow(a,2) *pow(b,2)* pow(c,2);
denominator(a,b,c)=-pow(a,4) - pow(b,4) - pow(c,4)+%
2*pow(a,2) *pow(b,2)+2*pow(c,2) *pow(b,2)+2*pow(c,2)*pow(a,2);]
beginscope[local bounding box=elli]
PgfmathtruncatemacroFPUmynumeratornumerator(a,b,c)
PgfmathtruncatemacroFPUmydenominatordenominator(a,b,c)
PgfmathtruncatemacroFPUmygcdgcdFPU(mynumerator,mydenominator)
messagenumerator=mynumerator,denominator=mydenominator,gcd=mygcd^^J
PgfmathtruncatemacroFPUnewnumeratormynumerator/mygcd
PgfmathtruncatemacroFPUnewdenominatormydenominator/mygcd
messagenew numerator=newnumerator,new denominator=newdenominator^^J
pgfmathtruncatemacromyprenum1
pgfmathtruncatemacromypreden1
foreach Prime in 2,3,5,7,11,13,17
pgfmathtruncatemacromyintintegerpower(newnumerator,Prime)
ifnummyint>1
pgfmathtruncatemacromyint2*int(myint/2)
PgfmathtruncatemacroFPUnewnumeratornewnumerator/pow(Prime,myint)
xdefnewnumeratornewnumerator
pgfmathtruncatemacromyprenummyprenum*pow(Prime,myint/2)
xdefmyprenummyprenum
fi
pgfmathtruncatemacromyintintegerpower(newdenominator,Prime)
ifnummyint>0
pgfmathtruncatemacromyint2*int(myint/2)
PgfmathtruncatemacroFPUnewdenominatornewdenominator/pow(Prime,myint)
xdefnewdenominatornewdenominator
pgfmathtruncatemacromypredenmypreden*pow(Prime,myint/2)
xdefmypredenmypreden
fi
messagenew numerator=newnumerator, pre num=myprenum,new
denominator=newdenominator, pre den=mypreden^^J
pgfmathsetmacromyr(myprenum/mypreden)*sqrt(newnumerator/newdenominator)
coordinate (A) at (0,0,0);
coordinate (B) at (c,0,0);
coordinate (C) at ((pow(b,2) + pow(c,2) - pow(a,2))/(2*c),sqrt((a+b-c) *(a-b+c) *(-a+b+c)* (a+b+c))/(2*c),0);
coordinate (T) at (c/2, c* (a*a + b*b - c*c)/(2*sqrt((a+b-c) *(a-b+c)* (-a+b+c)* (a+b+c))),0);
foreach point/position in A/left,B/below,C/right,T/below
fill (point) circle (1.8pt);
node[position=3pt] at (point) $point$;
beginscope[canvas is xy plane at z=0]
draw[thick] (T) circle (myr);
endscope
draw (T) -- (C) node[midway,sloped,fill=white] %
$displaystyleifnummypreden=1
myprenum
else
fracmyprenummypreden
fi
ifnumnewdenominator=1
ifnumnewnumerator=1
else
cdotsqrtnewnumerator
fi
else
ifnumnewnumerator=1
cdotfrac1sqrtnewdenominator
else
cdotsqrtfracnewnumeratornewdenominator
fi
fi,$cm;
endscope
node[above] at (elli.north)$a=a,b=b,c=c$;
endtikzpicture
enddocument
answered Aug 16 at 5:49
Schrödinger's catSchrödinger's cat
3,0515 silver badges13 bronze badges
edited Aug 16 at 14:55
answered Aug 16 at 5:49
Schrödinger's catSchrödinger's cat
3,0515 silver badges13 bronze badges
answered Aug 16 at 5:49
Schrödinger's catSchrödinger's cat
3,0515 silver badges13 bronze badges
answered Aug 16 at 5:49
Schrödinger's catSchrödinger's cat
3,0515 silver badges13 bronze badges
3,0515 silver badges13 bronze badges
I think, your answer is not automatically.
– minhthien_2016
Aug 16 at 5:58
Dunmo. I voted for your answer. But, your code doesn't true in every cases. E.G, triangle with lenght 6, 7, 8.
– minhthien_2016
Aug 16 at 10:34
Please try with sides 3, 4, 5. It is incorrect.
– minhthien_2016
Aug 16 at 10:36
Thank you very much.
– minhthien_2016
Aug 16 at 23:05
1
You can see package xintexpr.
– minhthien_2016
Aug 17 at 4:25
|
show 3 more comments
I think, your answer is not automatically.
– minhthien_2016
Aug 16 at 5:58
Dunmo. I voted for your answer. But, your code doesn't true in every cases. E.G, triangle with lenght 6, 7, 8.
– minhthien_2016
Aug 16 at 10:34
Please try with sides 3, 4, 5. It is incorrect.
– minhthien_2016
Aug 16 at 10:36
Thank you very much.
– minhthien_2016
Aug 16 at 23:05
1
You can see package xintexpr.
– minhthien_2016
Aug 17 at 4:25
I think, your answer is not automatically.
– minhthien_2016
Aug 16 at 5:58
I think, your answer is not automatically.
– minhthien_2016
Aug 16 at 5:58
Dunmo. I voted for your answer. But, your code doesn't true in every cases. E.G, triangle with lenght 6, 7, 8.
– minhthien_2016
Aug 16 at 10:34
Dunmo. I voted for your answer. But, your code doesn't true in every cases. E.G, triangle with lenght 6, 7, 8.
– minhthien_2016
Aug 16 at 10:34
Please try with sides 3, 4, 5. It is incorrect.
– minhthien_2016
Aug 16 at 10:36
Please try with sides 3, 4, 5. It is incorrect.
– minhthien_2016
Aug 16 at 10:36
Thank you very much.
– minhthien_2016
Aug 16 at 23:05
Thank you very much.
– minhthien_2016
Aug 16 at 23:05
1
1
You can see package xintexpr.
– minhthien_2016
Aug 17 at 4:25
You can see package xintexpr.
– minhthien_2016
Aug 17 at 4:25
|
show 3 more comments
draft saved
draft discarded
Thanks for contributing an answer to TeX - LaTeX Stack Exchange!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
To learn more, see our tips on writing great answers.
draft saved
draft discarded
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2ftex.stackexchange.com%2fquestions%2f504392%2fhow-can-i-show-radius-of-this-circle-exactly%23new-answer', 'question_page');
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
E.g.
draw (T) -- (C) node[midway,sloped,fill=white] $pgfmathprintnumbermyr$cm;.– Schrödinger's cat
Aug 16 at 5:03
@Dunno This is an approximate result. Can I get exactly result?
– minhthien_2016
Aug 16 at 5:07
pgfmathparsemyr xdefrpgfmathresult $r cm$– koleygr
Aug 16 at 5:23
@koleygr The approximate about
4.0414518843273803516. I want to exactly result.– minhthien_2016
Aug 16 at 5:27
1
@koleygr Yes.
frac73cdotsqrt3.– minhthien_2016
Aug 16 at 5:31