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Tag: right triangle

Posted on August 2, 2021

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.

Rational triangle

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Posted on December 18, 2020

A Paradoxical Zero-Length Hypotenuse

A strange right-triangle involving the unit imaginary number i

Zero-length hypothenuse

Posted on September 18, 2019September 18, 2019

A curious right triangle

The sides of a pentagon, hexagon, and decagon, inscribed in congruent circles, form a right triangle.

Posted on March 19, 2019March 19, 2019

Sangaku: Semicircle inscribed in a right triangle

Find the radius r of the semicircle inscribed in the right triangle below:


show solutionhide 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

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Recent Posts

  • Two Meanings, One Word: The Tautology Tango March 13, 2023
  • Fibonacci Zoetropes March 2, 2023
  • Arithmetic Mean ≥ Geometric Mean February 27, 2023
  • A Curious Constant January 26, 2023
  • Analog Binary-to-Decimal Converter January 11, 2023
  • Amazing Double Cube January 9, 2023
  • Harshad Years January 5, 2023

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Eye Bogglers
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You can't possibly color this
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Impossible Folding Puzzle and Other Mathematical Paradoxes
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