Mathematics Institute of the Triangle

08/26/2026

After years of searching, mathematicians have found dice that can allow five players to fairly decide who moves first in a board game, with a winner guaranteed from just a single roll

08/25/2026

Our school year has begun! We had a lovely school year kickoff party on Friday at Coco Chapel Hill with about 50 students and families. We had a big vegan spread of food and played Julia Robinson Mathematics Festival math games for all ages! Check out our catalog of classes at mathinst.com/catalog . (photo by Tamara Lackey)

08/15/2026

Math is beautiful and joyful and we try to illuminate that for all ages!

Math Is Beautiful ✨📐

Mathematics is more than numbers and equations—it is a language of patterns, symmetry, structure, logic, and elegance.

We see its beauty in the Fibonacci sequence, geometric symmetry, sine waves, fractals, tessellations, and identities such as

[
\boxed{e^{i\pi}+1=0}
]

which connects five fundamental mathematical constants in one remarkably compact equation.

Math reveals order in places that may initially look chaotic. Fractals show infinite complexity emerging from simple rules, while symmetry explains patterns found in crystals, architecture, physics, and nature.

Its beauty often comes from simplicity, universality, and unexpected connections—when one idea explains many seemingly unrelated phenomena.

Mathematics is beautiful because it turns patterns into understanding and complexity into structure.

08/13/2026

Do you know what Triangular Numbers are? Minity Maths has a video that explains them. Younger children can build bigger and bigger Triangular Numbers with objects; older children can explore algebraic techniques of working with them. Check out our handout mathinst.com/squareNumbers for Square and Triangular Numbers.

This video explains what triangular numbers are and the patterns as...

08/11/2026

In many math classes we focus on Euclidean geometry that assumes that we live on a flat earth; it works remarkably well in the small but parallel lines do meet on our round globe and in curved space, for example.

Different Geometries

08/10/2026

Renowned British mathematician G.H. Hardy once took a taxi to visit his collaborator, Indian mathematician Srinivasa Ramanujan, in the hospital.

Hardy noted that the taxi's number, 1729, seemed "rather dull," which prompted Ramanujan to respond that on the contrary, it was "very interesting" because it was the smallest number that could be expressed as the sum of two cubes in two different ways:

1729 = 1³ + 12³ = 9³ + 10³.

Numbers that can be expressed in this way have since been known as "taxicab numbers."

07/31/2026

International Infinity Day is on August 8 (8/8) and our friends at Counted Out are hosting a "first-ever, free virtual screening of COUNTED OUT, followed by a live conversation about the knowledge and confidence we need to navigate our world in an age of AI." The film addresses social justice and building confidence in math.

07/30/2026

We love teaching the Einstein Hat, Spectre, and other tesselations in our classes and math camps. In our new school construction, we are creating custom-cut Einstein Hats to fill a wall that students will see on entry.

The “hat” tile is a mathematical wonder. Discovered by amateur mathematician David Smith in 2022, it can be used to cover every square inch of an endless bathroom floor (or any other surface) without ever repeating a single pattern.

In a recent study, researchers in Japan have examined the tile’s physical properties in search of answers to a new question: Could it be useful in the real world, not just in a mathematical wonderland of infinite surfaces? http://spklr.io/6006EuTLG

07/29/2026

Prime numbers are the "atoms" of natural counting numbers 1, 2, 3, 4, 5, .... Wonder what prime and composite numbers are? Square numbers? Check out this NUMBEROCK song.

You're cordially invited to check out our growing library of math v...

07/28/2026

COLLATZ CONJECTURE : A MYSTERY OF MATHEMATICS 🌹❤️♥️

THE CONCEPTION OF COLLATZ, A STONEY PATH🌹❤️♥️

There is a unique way to confront assumption, it is through expressions that cause the initial value to drop below its value. The app that does this is (xo-t)*2^m. This can be proven number by number and verified has been up to about 5 million. But because it is so the transition step is still unknown obviously a pair orbit, for example we can see the number 10087 which is somewhat long in iterations until it reaches the expression (10087-2399)*2^3 for iteration 168 (The longest until observed, which equals the expression).

That is, in iteration 168 a connection occurs with the number 7688 via powers of 2, in this case 2^3. This alone is elegant, but the most interesting thing is raising the problem based on this. That is, if I start from the pure algebraic expression and replant a diophantic equation for example 3(2n+1)+1=((2n+1)-t)*2^m, what happens to the solutions?. Well these are in the form of a+2^ku where a is the starting value. For example, for the first iteration would be 5+2^2u, so such infinite solutions would be 5,9,13,... The search process is tedious and computer application.

In addition to iterations, you have to consider the parity chain of iterations, each of these presents a solution to a certain equation. The method would seem simple, for short iterations values it is not extremely complicated. But from certain iterations the thing changes a lot... The powerful thing about the method is that for iterations not more than 31 and not considering them all in iteration and parity you reach a coverage density more than excellent 93.16... %. But finding a structure step by step is very complicated and requires a lot of computational effort and even that 6.84.. % seems little, mathematically it's a lot. Would be interesting a computational effort but still a complicated undertaking.. As a personal comment we would say that Collatz's conjecture is more complex the more we want to know about it.