mathdeciphered

Passionate about helping students understand math. Mom to 1. Curriculum writer. Homeschool advocate. Coffee lover. Mentoring teachers in a small school in 🇺🇬.

[Paysages Mathématiques @paysmaths]

After 80 Years, Mathematicians Give Famed ‘Erdős Method’ an Upgrade
Source : Quanta Magazine / Leila Sloman

https://t.co/zW2JijdrUw
#mathematics #maths #math #podcast @QuantaMagazine

[Rafael Araujo @rafaela31416]

GEOMETRY
https://t.co/5F0aA6ji7r

[Mathematica @mathemetica]

Embedded in the rows of Pascal's triangle is a series that sums precisely to pi.

The yellow-highlighted binomial coefficients C(4,3)=4, C(6,3)=20, C(8,3)=56, C(10,3)=120, C(12,3)=220 form the denominators of the terms in
π = 3 + (2/3) · (1/4 − 1/20 + 1/56 − 1/120 + 1/220 − ⋯)

This identity adapts Nilakantha Somayaji's formula using entries from the triangle.

It is used to compute pi via summation of binomial reciprocals in computational mathematics and algorithm design.

[Mathematica @mathemetica]

Can a mechanical linkage turn linear constraints into a flawless, continuous orbit?

This mechanism is a variation of the Trammel of Archimedes (ellipsograph), featuring an extended multi-track base to smoothly guide two perpendicular slider pins.

As the shuttles travel back and forth along their fixed linear tracks, the end of the rigid arm maps out a mathematically perfect ellipse.
The parametric formula tracing this path is x = a cos(θ) and y = b sin(θ), where a and b represent the distances from the pen to each slider pin.

It is used to rout oval tables, cut custom picture frames, and guide mechanical cutting tools smoothly.

[Cliff Pickover @pickover]

Mathematics.

How to build a hyper-sandwich in four dimensions. Infinite possibilities. More dimensions. More deliciousness. The only limit is reality. (And maybe your appetite.)

Credit: Image sent to me by Dan a Rama, @Dan_a_rama, June 18, 2026.

[MIT CSAIL @MIT_CSAIL]

The hidden patterns & math behind Pascal’s Triangle, v/@mathemetica.

[Mathematica @mathemetica]

Deriving the quadratic formula by completing the square, shown step by step.

- Start with ax² + bx + c = 0.
- Divide by a
- Move the constant to the right
- Add (b/2a)² to both sides
- Simplify the right side to (b² - 4ac)/4a²
- Take square roots
- Solve to reach x = (-b ± √(b² - 4ac)) / (2a)

It is used to calculate the path of a projectile like a thrown ball or to find break-even points in business where costs and revenue follow a parabolic curve.

[Mathematica @mathemetica]

Curious what a “named graph” looks like?

This gallery presents 35 classic examples from graph theory; including Balaban cages, Chvátal graph, Moser spindle, Meredith graph, and Tutte graph; each chosen for distinctive structural properties like regularity, symmetry, girth, or chromatic number.

The theory and the graph behind them power computer network routing, circuit board design, social media analysis, molecular modeling in chemistry, and optimization algorithms in logistics and computing.

[Cliff Pickover @pickover]

Mathematics.

This is a walkable trefoil knot.

© Dr. Robert Fathauer, @RobFathauerArt, Used with permission, https://t.co/GAbWFfBk82

[Dr. Tara Taylor @tara_taylor]

Look at the spirals in the daisy! 😍

[Cliff Pickover @pickover]

Mathematics. It's alive!

In cellular automata, such as Conway's Game of Life, a Breeder is a pattern that generates copies of a secondary pattern, each of which then generates copies of a tertiary pattern. https://t.co/sSkFlwn6k9

[Mathematica @mathemetica]

The Koch curve is constructed iteratively from a straight line segment.

Order 0 (Initiator): straight line, length = 1
Order 1 (Generator): length = 4/3
Order 2: length = 16/9
Order 3: length = 64/27

With each order, every straight segment is replaced by four segments each one-third as long, multiplying the total length by 4/3. As n → ∞, length → ∞.

[Howie Hua @howie_hua]

Today's date is 6/7 so let's talk about how cool the decimal representation for sevenths is.

[Physics In History @PhysInHistory]

The book of nature is written in the language of mathematics.

– Galileo Galilei

[Math Files @Math_files]

The ancient Babylonians used a base-60 number system rather than base-10, which is why we still have 60 seconds in a minute, 60 minutes in an hour, and 360 degrees in a circle today.

[mathdeciphered @mathdeciphered]

@Just_Maths Yay!

[mathdeciphered @mathdeciphered]

@ReviseJustMaths @Just_Maths Following along! Always looking for new accounts.

[Physics In History @PhysInHistory]

Standard normal distribution church

[Math Files @Math_files]

It is fun to take a short historical side trip dealing with series. The famous mathematician Carl Friedrich Gauss was ten years old when he attended his first day of a particular mathematics class. The instructor, an odd curmudgeon, liked to give himself a rest from lecturing by assigning his students a tedious problem to occupy their time. As the students finished their work on their small slate boards, they would place them on the instructor's table. When all the slate boards had been stacked on top of each other, the instructor could see who had finished first and who was last.

On this particular day, he gave them the following problem: add the first 100 natural numbers together.

Gauss immediately wrote an answer on his slate board and placed it on the table. The instructor was incredulous that this new student could add 100 terms so quickly and assumed that the answer would be wrong. However, when all the other students had finally finished their work and placed their slates on the table, the instructor turned over Gauss's slate and read the correct answer: 5050.

How had Gauss done it?

Gauss noticed that the first term, 1, and the last term, 100, added together to make 101. Then he realized that the second term, 2, and the next-to-last term, 99, also added to 101. In fact, by continuing this pattern, he found 50 pairs of numbers, each summing to 101. Fifty multiplied by 101 is 5050.

We have no record of the words uttered by the shocked teacher when he realized that young Gauss was correct.