Happy Perfect-Square New Year 2025

As I write this, the new year, 2025, has already come to parts of the world. It arrives here, where we’re on Chicago time, in about four and a half hours. This new year is the first perfect-square year since 1936, and there won’t be another one until 2116.

Since 45 = (9)(5) = (3^2)(5), and 2025 is the square of that, the prime number factorization of the new year is (3^4)(5^2).

Happy New Year to all!

A Tessellation Featuring Three Varieties of Squares

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Oblique All-Square Tessellation #2

The first of these used the center of a square as the center of rotation. This one, by contrast, uses an intersection as the center of rotation. In each case, 45 degrees is the angle used.

An Oblique All-Square Tessellation

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Tessellation of Squares of Two Sizes

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squares

A Tessellation of Star Octagons, and Two Sizes of Squares

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tessellation of star octagons and two sizes of squares

Octagons, Hexagons, and Squares

octagons hexagons squares

This Space Station for Geometricians Has, as Outer Hulls, Twelve Trapezoids, and Six Parallelograms with One Square Window / Docking Port Each

12 Trapezoids -- and six parallelograms with square windowsl

I can’t think of any good reasons for geometricans not to have their own space station, and I know what we’d do there:  we’d work on geometry (also known informally as “playing with shapes”).

My suggestion for this space station’s design was created with Stella 4d, and you may find that program (to try or guy) here:  http://www.software3d.com/Stella.php.

A Tessellation Using Regular Octagons, Squares, Rhombi, and Non-Convex, Equilateral Hexakaitriacontagons

Regular Octagons Squares Rhombi and Nonconvex Hexakaitriacontagons

Tessellation Featuring Squares, Regular Hexagons and Dodecagons, and Thirty Degree Rhombi

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