Category Archives: Math Beauty

Expression: (x+y+z)(x^5+y^5+z^5) – (x^3+y^3+z^3)^2

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Triangle relation

  If D is the area of a triangle ABC show that and                                

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Pythagorean triples – shortest leg is prime

  All the prime numbers less than 1000: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, … Continue reading

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Square numbers with two different digits

      Can you find other examples?                    

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How 4 successive Fibonacci numbers relate to right triangles

                               

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Pythagorean triples | Ratio = Area/Perimeter = 1,2,3,…,25

                     

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Primitive Pythagorean triples – curious properties

  Here are all the primitive Pythagorean triples with   c ≤ 300 : In column (1) :   the primitive Pythagorean triples In column (2) :   the sum of the hypotenuse and one of the legs of a … Continue reading

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Num3er of ways of representing any integer N as a sum of 3 distinct positive integers

  In how many ways can you express any integer n as a sum of 3 distinct positive integers? that is, where   a,   b   and   c   are distinct positive integers.   For example, There’s only … Continue reading

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Repdigit | Legs of Pythagorean triples: 111,222,…,999

  Repdigit | Legs of Pythagorean triples : 11, 22, …, 99                      

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Repdigit | Pythagorean triples – Hypotenuse: 55,…,9999

                     

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