The sum of the first n odd integers is n². Viewed on a tetrahedron.

Author:
Vincent Pantaloni
Topic:
Addition, Integers, Sequences and Series, Solids or 3D Shapes

Animated GIF

Animated GIF
The sum of the first n odd integers is n². 1+3+5+...+(2n-1)=n². Animated 3D visualization on a tetrahedron.

GeoGebra applet

Proof without words

The sum of the first n odd integers is n². 1+3+5+...+(2n-1)=n².

By transforming rows with consecutive odd number of dots (1, 3, 5, etc) into a square I realized it looked like a 3D view of a tetrahedron, so I made this visualization. See here : geogebra.org/m/wbunwkkg

Which led to this smaller version with a better animation

https://www.geogebra.org/m/kfquc2vb

GIF

GIF
https://www.geogebra.org/m/kfquc2vb

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