Revision #899 → #1507 · back to history
addedPythagorean triple56154f9a093e
added(3, 4, 5) is a Pythagorean triplef48b4d435e58
addedScaling a Pythagorean triple2f98112bb10a
addedPythagorean trianglea4d160a4faa8
addedPrimitive Pythagorean triple177069dbbf20
added(3,4,5) primitive vs (6,8,10) not533b33bce8c5
addedEvery triple scales to a unique primitive0a580f76c001
addedPythagorean theorem5f22edc057c1
addedNon-integer right trianglef5ca09a45ce7
addedDiophantine equation4d6df484773f
added16 primitive triples up to 100fa8dbfc76891
addedEuclid's formulad4e0be17e07e
addedPrimitivity condition in Euclid's formula8a6e8368b606
addedEvery primitive triple from coprime pair282d46cd98a2
addedInfinitely many primitive triplesded8d54192a2
addedExtended formula with parameter ke4b84ca9ffb5
addedConsecutive Pell numbers give a,b differing by 1481258d91421
addedSufficiency of Euclid's formula56b08a222795
addedNecessity of Euclid's formula992259e2902c
addedInterpretation of parameters2883d8606b2f
addedSymmetric variant of Euclid's formula7a7572f073ce
addedMerged unique formula without exchange9e155357a187
addedPerfect square propertyf1649b6c290f
addedAt most one square among a,b,c9a1dcba76c0b
addedArea not a square or twice a squarec6b999cf98e2
addedExactly one leg is even, hypotenuse odd35f219037088
addedExactly one leg divisible by 3a3278ae7d481
addedExactly one leg divisible by 46defea401c9d
addedExactly one of a,b,c divisible by 5249eaeb92bed
addedLargest divisor of abc is 606703710b32f5
addedOdd numbers as odd leg9f7bc76ae4fe
addedEven leg divisible by 46a1cf0e06657
addedHypotenuse form 4n+1fd10a1207685
addedArea is congruent number divisible by 659b7d0828e7b
addedIncircle and excircle radii integer16c3939770f6
addedCircumdiameter equals hypotenuse1ac6d1873f6d
addedDescartes Circle Equation from curvatures561ed6f620da
addedOuter Soddy radius equals semiperimeter6136bc79570f
addedTwo prime sides at mostfeb7d255cd67
addedOnly one side can be a perfect powerfd75846b2502
addedFermat's right triangle theoremfd8e457db2c3
addedUnique area-to-squared-semiperimeter ratiofafde608bd59
addedNo integer altitude from hypotenusebcff37ce9700
addedPrimitive triples form a rooted ternary tree657d8769afef
addedAcute angles not rational degreesc7d1d1109639
addedIntegers not 2 mod 4 are in primitive tripleb8e7e50d96e5
addedEvery integer >2 in some triple3e0c1381421c
addedHypotenuse and longest leg differ by one181bfe8a35b1
addedHypotenuse and longest leg differ by twoea9c77e65bf8
addedDiffer by 2k^203fa29e10544
addedTwo legs differ by one3ef5684fc2a0
addedk triples with same area336a8cd30303
addedk primitive triples with same lege9f3f0a6101e
addedk triples with same hypotenusec029bab7bc33
addedPrime power hypotenuse conditionfe19d62f1515
addedHypotenuse characterization by prime factorsc527085988a9
addedFermat's square hypotenuse triple48db99a1b01b
addedNon-primitive triples with integer altitudef2fc5d2cbbb4
addedCorrespondence: rational points and primitive triplesc3df9e46b4d8
addedParametric equation of unit circle and Euclid's formulaaf49f35fb98a
addedStereographic projection establishes rational correspondencedbd4a192abea
addedUnit circle is a rational curve133717f3a40d
addedLattice points interior to Pythagorean triangle38435af200e2
addedFirst coincidence of triples sharing areaf9c560968841
added1-to-1 mapping rationals to primitive triples6dc03861521e
addedMatrix encoding of Pythagorean triplesbf765594bdb4
addedSpinor outer product encodes primitive triple207d049d6591
addedModular group94d6501c536c
addedModular group transitive on standard triplesfa29f2db5e85
addedΓ(2) transitive on primitive triples4448de808296
addedΓ(2) is free group generated by U and L194896d0df29
addedBerggren's parent/child relationships79a1f0ad107f
addedFactoring in Gaussian integersf9ac28762426
addedz and z* are squares of Gaussian integers3216a6d7f531
addedSquare of Gaussian integer gives Euclid's formula62367f2db54d
addedPrime Gaussian square iff prime hypotenuse19993fc92619
addedParabolic patterns of triplesf181b64a1f9e
addedPlatonic sequence (odd a, Pythagoras)2c4a50dcf62c
addedPlatonic sequence (even a, Plato)9f56332aaa0f
addedAll triples from Platonic sequence with rational a9a4de2124b49
addedJacobi–Madden equation equivalence7b311ddd3d80
addedParametrization of equal sums of two squares6b761b96a9b5
addedEuler's solution for equal productsf0dcb801ed8a
addedDescartes' Circle Theorem equivalence to three triples6cce3f3a7ff3
addedNo isosceles Pythagorean triplesa2458e354c22
addedAlmost-isosceles parametrization via Pell7b5666bfd59f
addedRecursive Pell solutiond88a38df2d93
addedLonger leg and hypotenuse differ by onea5ea9149139d
addedAll odd numbers appear in this typec5457adb34e7
addedFibonacci-based Pythagorean hypotenuses932fa9a47815
addedPythagorean n-tupled1dc6f608835
addedEvery primitive n-tuple from this approachfbf946cff2bd
addedSum of k consecutive squares formula14c8bce3226a
addedCannonball-stacking problem of Lucas548ac0907086
addedFermat's Last Theorem4c34a9fd37bc
addedSmallest sequences for n=3,4,5,7,898e34a242cd1
addedRamanujan 1729240c1aa68829
addedCounterexamples to Euler's sum of powers conjecturee171ab470ce8
addedHeronian trianglefefecdcd80ed
addedEvery Pythagorean triple is Heronian228416a23cb4
added(4,13,15) Heronian but not Pythagoreancc281d69dee9
addedHeron condition for integer triple3c9400b38fbe