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Monthly Archives: October 2016
tan A = tan B + tan C + tan D
Find other 4-tuples of distinct integers between and that satisfy the relation Other solutions: How many such equations can you produce if we allow repeated angles? … Continue reading
Triangle (a,b,c) – inradius and circumradius — (Part 2)
Establish the following For any triangle , and where is the circumradius, the inradius and the semiperimeter. Then are in geometric progression iff … Continue reading
Triangle (a,b,c) – inradius and circumradius — (Part 1)
Establish the following For any triangle , and where is the circumradius, the inradius and the semiperimeter. Then are in arithmetic progression iff … Continue reading
Pythagorean triple(a,b,c); integer solutions of the equation a^2 + ab + b^2
The integers form a Pythagorean triple. There are similar formulas for integer solutions of the equation It can be verified that satisfy the equation If x and y are integers, then … Continue reading
Right triangle in a rectangle
An infinite number of rectangles may be generated, each with a right triangle inscribed as shown: such that the lengths of the sides of the various right triangles are integers. ***************************************** … Continue reading
Primitive Pythagorean triples- radius of incircle is a square
The radius of incircle is a square – up to the value of … Continue reading
Set of 3 Pythagorean triangles equal perimeters and area in A.P.
Here are sets of 3 Pythagorean triangles with equal perimeters and area in arithmetic progression. Note that the perimeters are multiples of 120. The pattern breaks in this example: The perimeter is not a multiple of … Continue reading
Part 2 – PT diff. between sides,perim,diam. of inscribed circles are squares,diff. between Areas a cube
Part 1 – Pythagorean triangles diff. between sides,perim,diam. of inscribed circles are squares,diff. between Areas a cube Find two Pythagorean triangles and such that are all squares And, the difference of areas a cube … Continue reading
Pythagorean triangles – shortest leg, longest leg
Find all values of a positive integer constant such that and describe the two legs of a Pythagorean triangle for every positive integer value of . Let n = … Continue reading
Fun With Num3ers 