Triangle Radicals
Initializing live version
Requires a Wolfram Notebook System
Interact on desktop, mobile and cloud with the free Wolfram Player or other Wolfram Language products.
An integer-sided triangle always has an area of the form , where is a square-free number and is an integer. Denote , which appears under the radical sign, as the "radical of the triangle".
[more]
Contributed by: Ed Pegg Jr (May 2016)
Open content licensed under CC BY-NC-SA
Snapshots
Details
For all triangles with a given square-free radical , the value is also divisible by the term of , where (mod12).
In the Demonstration "Wheel Graphs with Integer Edges", it was shown that all small integer-edge wheel graphs use triangles of two or fewer radical types.
Permanent Citation