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Monthly Archives: February 2016
RootMeanSquare Primitive Triangle(a,b,c) such that a^2 + c^2 = 2b^2
RootMeanSquare http://mathworld.wolfram.com/RootMeanSquare.html parametric representation of all primitive solutions of the Diophantine equation: , where are relatively prime, with and an integer Perimeter where : OR … Continue reading
(xn)^3 + (xn+1)^3 + … + x^3 + (x+1)^3 + … + (x+n)^3
An integer of the form is called a Triangular number. In general:
Posted in Number Puzzles
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Heronian triangles with one side Even of length a = 4,6,8,10 –(Part 2)
Heronian triangles with one side odd of length a = 3,5,7,9,11 (Part 1) There are infinitely many of primitive Heronian triangles with one side of length a > 2 If is … Continue reading
Heronian triangles with one side odd of length a = 3,5,7,9,11
There are infinitely many of primitive Heronian triangles with one side of length a > 2 if is odd : the other sides are: , where is a solution of the Pelian … Continue reading
Puzzle  convex quadrilateral
Find a convex quadrilateral such that the quadrilateral has the smallest area and all four of its sides (a, b, c, d), two diagonals (e, f) and area K are : (1) distinct integers (2) … Continue reading
Nested trigonometric functions: sine and cosine
and Why is always greater? And, Does the ratio depend on ? … Continue reading
Median AD in any triangle ABC
Prove that in any triangle , where is a median and
Diophantine equation: (x^8 + y^8 + z^8) = 2(x^16 + y^16 + z^16)
Find integer solutions to
A 4×4 matrix containing distinct integers ≤ 27
Here’s a 4×4 matrix that contains distinct integers ≤ 27 whose row sums are the same : 1 + 2 + 18 + 24 = 45 8 + 15 + 10 + 12 = … Continue reading