Pythagorean Triples
Wikipedia shows the formula
–
MathType@MTEF@5@5@+=feaaguart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqefmuySLMyYLgaiuaajugybabaaaaaaaaapeGaa83eGaaa@3A6F@
like so.
A Pythagorean triple consists of three positive integers a,
b, and c, such that a2 + b2 =
c2.
Personally, I prefer
my own format, my classic.
x
2
+
y
2
=
z
2
,
x
2
+
y
2
=z
MathType@MTEF@5@5@+=feaaguart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiEamaaCaaaleqabaGaaGOmaaaakiabgUcaRiaadMhadaahaaWcbeqaaiaaikdaaaGccqGH9aqpcaWG6bWaaWbaaSqabeaacaaIYaaaaOGaaiilamaakaaabaGaamiEamaaCaaaleqabaGaaGOmaaaakiabgUcaRiaadMhadaahaaWcbeqaaiaaikdaaaaabeaakiabg2da9iaadQhaaaa@4536@
Providing x, y, and z are all Integers and positive in
nature.
By the way, the “comma” stands for “and.”
Now, the way, I define Pyats a little different. What if?
|
|
x+A=y,y+B=z
MathType@MTEF@5@5@+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiEaiabgUcaRiaadgeacqGH9aqpcaWG5bGaaiilaiaadMhacqGHRaWkcaWGcbGaeyypa0JaamOEaaaa@3FF7@
|
|
x
2
+
(x+A)
2
=
(y+B)
2
MathType@MTEF@5@5@+=feaaguart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiEamaaCaaaleqabaGaaGOmaaaakiabgUcaRiaacIcacaWG4bGaey4kaSIaamyqaiaacMcadaahaaWcbeqaaiaaikdaaaGccqGH9aqpcaGGOaGaamyEaiabgUcaRiaadkeacaGGPaWaaWbaaSqabeaacaaIYaaaaaaa@43A5@
Wikipedia Reference: http://en.wikipedia.org/wiki/Pythagorean_triple