Lagrange's Four-Square Theorem Seen Using Polygons and Lines

Any natural number can be represented as the sum of the squares of four non-negative integers. For most numbers there are multiple representations. In this Demonstration the four integers (not squared) may be viewed using three different options.1. For each set of four numbers a polygon is displayed with vertices and .2. Each set is sorted from smallest to largest. The first two numbers a;;

Lagrange's Four-Square Theorem Seen Using Polygons and Lines

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Lagrange's Four-Square Theorem Seen Using Polygons and Lines - Wolfram Demonstrations Project

Dotted lines indicate original control polygon while continuous curves

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Cloud, Newton polygon and some supporting lines of P in (2)

Lagrange's Four-Square Theorem Seen Using Polygons and Lines - Wolfram Demonstrations Project

Mathematics, Free Full-Text

Lagrange's four-square theorem

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Plane of normal (a,b,c) Download Scientific Diagram