Did you know? When you calculate (π^{4}+π^{5})/e^{6}, you get around 1! This means a triangle with sides π^{2}, e^{3}, and √π^{5} is nearly a right triangle…

## Egguation

Solve for the perfect omelette with this eggcellent formula!

In fact, if you graph x^{2} + y^{2} = 2^{y}, you will obtain a flawless egg shape:

However, there are also other methods to create a perfect ovoid shape using a compass and ruler, as illustrated below.

## Pervasive Pi: Unveiling the Quantum Connection

The formula developed by British mathematician John Wallis defines π as an infinite product of integer ratios. This formula was recently discovered in a quantum mechanics equation for hydrogen atom energy states, emphasizing its pervasiveness in math and science.

More number facts.

## Only For Geniuses

To correct this equality, simply toggle ONE pixel!

## Set Theory ⋃ Humor

Practical examples of intersection and union…

## Averaging square roots

Is the average of two square roots less than, equal to, or greater than the square root of the average?

## Lateral Mathematics

High math skills are required to solve this puzzle…

Fill in the three boxes below using any of the following numbers: 1, 3, 5, 7, 9, 11, 13, 15.

You are allowed to repeat the numbers.

## The Geometry of the Bees

When constructing a honeycomb, bees aim to minimize wax usage and honey consumption, using the least wax necessary for a comb with maximum honey storage. The wax cells are designed with interlocking opposing layers, sharing facets at closed ends while having open ends facing outwards (see fig. 1). Each cell is a ten-sided structure with a rhombic decahedron form – a hexagonal prism with three rhombi at its closed end (fig. 2). Mathematicians have extensively studied the highly efficient isoperimetric properties of these cells. The question remains: What angle alpha maximizes volume while minimizing surface area on each cell face when the hexagonal prism’s faces have a width of 1 unit?

Continue reading “The Geometry of the Bees”## Summation Formulas

Some remarkable summation formulas…

## φibonacci formula

Because F* _{n}*→ φ

*ⁿ*when

*n*→ ∞