These are two proofs for why prime numbers revolve around multiples of 4 and multiples of 6. #math #maths #mathematics #algebra #arithmetic

This is one of my favorite numeric truths and it has a pleasant geometric interpretation to go with it. Take three squares and construct the diagonals as shown in the diagram. The product of the length of the two shorter diagrams is equal to the length of the longest diagonal. #math #maths

Assuming the unknowns are integers, then the following rules for parity addition and parity multiplication holds true. Parity is the state of an integer when it’s divided by 2. All integers take the form of either 2x (even) or 2x+1 (odd) where x is any integer. #math #maths #mathematics

The sum of two squares times the sum of another two squares equals the sum of yet another two squares. These formulae are used to find examples like 5 × 13 = (2²+1²) × (2²+3²) = 65 = 8²+1² = 7²+4². #math #maths #mathematics #algebra #arithmetic

Two proofs of a result that’s based around prime numbers. For example, 11² - 1 = 120 = 24×5. #math #maths #mathemati cs #algebra #arithmetic

Here’s another classic proof of the Pythagorean Theorem where four triangles are placed in such a way that a small square in the middle of them. From there, an equating of areas occurs. #math #maths #mathematics #geometry #trigonometry

This is an augmented version of the first proof discovered by US President James Garfield. By slicing the original diagram in half, a trapezoid is created with three right triangles overlaying it so an equating of areas can occur. #math #maths #mathematics #geometry #trigonometry

This is one of my favorite geometric proofs. It’s basically a square that’s twisted into a larger square so an equating of areas occurs. #math #maths #mathematics #geometry #trigonometry

Given an isosceles triangle and a cevian that splits the base into two smaller segments, then the following relation is true. This is proven using the Pythagorean theorem twice. #math #matha #mathematics #geometry #trigonometry

Given two real numbers a, b such that a > b, then then the difference of squares will equal the product of the two numbers. This formula was used for centuries to calculate large products. #math #maths #mathematics #algebra #arithmetic

Proof that the cosecant of the Brocard angle in the heptagonal triangle is 2√2. #math #maths #mathematics #geometry #trigonometry

Proof that the cotangent of the Brocard angle in the heptagonal triangle is √7. #math #maths #mathematics #geometry #trigonometry

The cotangent of the Brocard angle in a triangle is equal to the sum of the cotangents of the triangle’s angles. #math #maths #mathematics #geometry #trigonometry

The Brocard angle ω in a triangle. L₁, L₂, L₃ are the lengths of the segments from the Brocard point to the vertices. a, b, c are the side lengths of the triangle. A, B, C are the angle measures of the triangle. #math #maths #mathematics #geometry #trigonometry

ω is the Brocard angle of ΔABC. a, b, c are the side lengths of the triangle. A, B, C are the angle measurements of the triangle. L₁, L₂, L₃ are the lengths of the segments between the Brocard points and the vertices. #math #maths #mathematics #geometry #trigonometry

ω is the Brocard angle of the triangle. A, B, C are the angle measures of the triangle. a, b, c are the side lengths of the triangle. L₁, L₂, L₃ are the lengths between the vertices and the Brocard point (labeled D). #math #maths #mathematics #geometry #trigonometry

Some more triangle area and angles identities derived from prior results. #math #maths #mathematics #geometry #trigonometry

Every acute triangle can have its sides written in terms of the other sides and the cosines of the angles adjacent to that side being solved for. #math #maths #mathematics #geometry #trigonometry

These are area formulae for any triangle given the side lengths, the circumradius and the angle measurements. #math #maths #mathematics #geometry #trigonometry

Given any triangle, the area of it can be found using the sides and the circumradius. This derivation of the formula isn’t a standard one, but it’s a fun one nonetheless. #math #maths #mathematics #geometry #trigonometry