Segitiga sama sisi: Perbedaan antara revisi

* <math>\displaystyle a=b=c</math>

* <math>\displaystyle a^2+b^2+c^2=ab+bc+ca</math> <ref name=Andreescu/>

* <math>\displaystyle abc=(a+b-c)(a-b+c)(-a+b+c)\quad\text{(Lehmus)}</math><ref name=Cosmin/>

* <math>\displaystyle (a+b+c)\!\left(\frac{1}{a}+\frac{1}{b}+\frac{1}{c}\right)=9</math> <ref name=AoPS2016>[http://www.artofproblemsolving.com/community/c6t48f6h1315155_geometryprove]</ref>

* <math>\displaystyle \frac{1}{a}+\frac{1}{b}+\frac{1}{c}=\frac{\sqrt{25Rr-2r^2}}{4Rr}</math> <ref>{{cite journal|last1=Bencze|first1=Mihály|last2=Wu|first2=Hui-Hua|last3=Wu|first3=Shan-He|title=An equivalent form of fundamental triangle inequality and its applications|journal=Research Group in Mathematical Inequalities and Applications|date=2008|volume=11|issue=1|url=http://rgmia.org/papers/v11n1/equivalent.pdf}}</ref>

* <math>\displaystyle s=2R+(3\sqrt{3}-4)r\quad\text{(Blundon)}</math><ref>{{cite journal|last1=Dospinescu|first1=G.|last2=Lascu|first2=M.|last3=Pohoata|first3=C.|last4=Letiva|first4=M.|title=An elementary proof of Blundon's inequality|journal=Journal of inequalities in pure and applied mathematics|date=2008|volume=9|issue=4|url=http://www.emis.de/journals/JIPAM/images/220_08_JIPAM/220_08_www.pdf}}</ref>

* <math>\displaystyle s^2=3r^2+12Rr</math> <ref>{{cite journal|last1=Blundon|first1=W. J.|title=On Certain Polynomials Associated with the Triangle|journal=Mathematics Magazine|date=1963|volume=36|issue=4|pages=247–248|doi=10.2307/2687913}}</ref>

* <math>\displaystyle s^2=3\sqrt{3}T</math> <ref name=Alsina>{{cite book|last1=Alsina|first1=Claudi|last2=Nelsen|first2=Roger B.|title=''When less is more. Visualizing basic inequalities|date=2009|publisher=Mathematical Association of America|pages=71, 155}}</ref>

* <math>\displaystyle s=3\sqrt{3}r</math>

* <math>\displaystyle s=\frac{3\sqrt{3}}{2}R</math>

* <math>\displaystyle A=B=C=60^\circ</math>

* <math>\displaystyle \cos{A}+\cos{B}+\cos{C}=\frac{3}{2}</math>

* <math>\displaystyle \sin{\frac{A}{2}}\sin{\frac{B}{2}}\sin{\frac{C}{2}}=\frac{1}{8}</math> <ref name=Cosmin/>

* <math>\displaystyle A=\frac{a^2+b^2+c^2}{4\sqrt{3}}\quad</math> ([[ketidaksamaan Weitzenböck|Weitzenböck]]) <ref>{{cite web|last1=McLeman |first1=Cam |last2=Ismail |first2=Andrei |title=Weizenbock's inequality |url=http://planetmath.org/encyclopedia/WeizenbocksInequality.html |website=PlanetMath |deadurl=yes |archiveurl=https://web.archive.org/web/20120218055252/http://planetmath.org/encyclopedia/WeizenbocksInequality.html |archivedate=2012-02-18 |df= }}</ref>

* <math>\displaystyle A=\frac{\sqrt{3}}{4}(abc)^{^{\frac{2}{3}}}</math> <ref name=Alsina/>

* <math>\displaystyle R=2r\quad\text{(Chapple-Euler)}</math><ref name=Andreescu/>

* <math>\displaystyle 9R^2=a^2+b^2+c^2</math> <ref name=Andreescu/>

* <math>\displaystyle r=\frac{r_a+r_b+r_c}{9}</math> <ref name=Cosmin>{{cite journal|last1=Pohoata|first1=Cosmin|title=A new proof of Euler's inradius - circumradius inequality|journal=Gazeta Matematica Seria B|date=2010|issue=3|pages=121–123|url=http://rms.unibuc.ro/gazeta/gmb/2010/3/articol.pdf}}</ref>

* <math>\displaystyle r_a=r_b=r_c</math>