Did you know? When you calculate (π4+π5)/e6, you get around 1! This means a triangle with sides π2, e3, and √π5 is nearly a right triangle…
Nearly Right
Right Triangle with Rational Sides
The simplest right triangle with rational sides (the longest side has a denominator of 45 digits!) and area 157, was found by Don Zagier in 1993.
A Paradoxical Zero-Length Hypotenuse
A strange right-triangle involving the unit imaginary number i
A curious right triangle
The sides of a pentagon, hexagon, and decagon, inscribed in congruent circles, form a right triangle.
Sangaku: Semicircle inscribed in a right triangle
Find the radius r of the semicircle inscribed in the right triangle below:
Show solution
The altitude h of the right triangle is:
h = 6 · 8/10 = 4.8
By similarity:
4.8/r = 8/(8-r)
Thus
r = 3
