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Exploring the Math Behind the FIFA 2026 Trionda Ball

Mon, 06 Jul 2026 19:28:42 Z

Every four years, the world comes together to watch one of the most anticipated sporting events in history: the FIFA World Cup.

Behind all the anticipation, venue planning, and media fanfare, there are many artists and researchers who devote themselves to designing a new FIFA World Cup ball to be rolled out for the public eye (pun intended).

This post presents an overview of the geometric ideas behind the design of the FIFA 2026 "Trionda" ball, using Maple to visualize and explore these concepts in depth. The ideas presented here were inspired by this Scientific American Article. For more information and facts about the 2026 Trionda ball, as well how the shape of the ball impacts play on the pitch, I suggest you check it out!

FIFA ball designs are often inspired by one of the 5 Platonic solids. A Platonic solid is a convex polyhedron with each face being the same regular polygon with the same number of faces meeting at each corner.

This year, the Trionda ball was constructed from the simplest of these shapes, the tetrahedron, consisting of 4 triangles, with 3 faces meeting at each corner. Of the five Platonic solids, this shape has the fewest faces, making it the least sphere-like. Turning such a simple polyhedron into a smooth ball is therefore a surprisingly challenging geometric problem.

So how can we turn our pointy tetrahedron into something that rolls? Rather than trying to transform the entire tetrahedron at once, we can start by redesigning a single triangular face. The goal is to create a curved triangle that will fit perfectly with three identical copies of itself while covering the surface of a sphere.

Fermat sequence and similar sequences

Mister_Matthew_abc — Fri, 03 Jul 2026 15:56:05 Z

Hi Maple community and others,

I'm very proud to present my code.

Sequences are fun,
for those who know, about them

consider Fermat numbers, of the form,
F(n) = (2^(2^n)) + 1.
goes like

3, 5, 17, 257, 65537, 4294967297, 18446744073709551617,
340282366920938463463374607431768211457, ...

in oeis.org database at
https://oeis.org/A000215 .

Similarly we can have base 3,

B(a) = (3^(3^a)) + 1.
goes like, this,
4,28,19684, ...
online, in database, with Universal Resource Location (URL)
https://oeis.org/A129290

There could also be base 4, that grows even faster

double_exponential_2_and_3_and_4.mw

That is all that I have, for now.

Thank you for this free forum.
regards,
Matt

Matt's explore about Andrica's conjecture

Mister_Matthew_abc — Fri, 03 Jul 2026 10:19:45 Z

Hi Maple community, and all,

Here is a little Maple worksheet, shoing an interesting property of prime numbers.

Numerical evidence supports Andreca's conjecture.

see

_Andricas_conjecture.mw

good fun

see, also
Andrica's Conjecture -- from Wolfram MathWorld
Enjoy
regards,
Matt

PS online at https://MattAnderson.fun/

PPS Have a good day, everybody.

Math Success in the Age of AI: Introducing the Maplesoft Math Success Platform

Karishma — Thu, 02 Jul 2026 19:06:37 Z

Last week, we launched the Maplesoft Math Success Platform.

This launch reflects a lot of conversations I’ve had over the past year with educators and institutions about what it means to teach and learn math in the age of AI.

Math Education in the Age of AI

At first, many of those conversations were about visibility. If students were completing homework, quizzes, and other assessments with help from AI, those results became harder to interpret. Did students understand the work, or had they copied down a solution that made sense in the moment without building the understanding needed to do something similar on their own?

That visibility still matters.

Over time, though, those conversations led to a more nuanced conclusion. The question is not simply how we prevent students from taking shortcuts. It is how we help them develop the mathematical judgment, intuition, and critical thinking they will need in a world where AI is part of how they learn and work.

In some ways, that has become even more important. When answers are easy to generate, students need to be able to test ideas, recognize when something does not make sense, explain their reasoning, and trust their own thinking.

The Maplesoft Math Success Platform

That is why I am proud to share the launch of the Maplesoft Math Success Platform.

Built on Maple, the platform brings together our math technology and extends it with analytics, AI-driven insights, targeted resources, and content expertise to help institutions support math learning in a more complete way.

It gives instructors and learning support teams better insight into where students are struggling, supports the creation of better questions and learning experiences, helps students move beyond the answer, and helps institutions respond to a world where AI is now part of how students practice, study, and get help.

You can learn more about the Maplesoft Math Success Platform on our website.

We also wrote more about the thinking behind this launch in our new whitepaper, Math Education in the Age of AI: From Grading Answers to Understanding Student Progress. It looks at why math education needs a new approach in the age of AI: one that helps instructors ask better questions, create learning experiences that build understanding, and use learning signals to see where students need support.

I’d love to hear what you think. How are you seeing AI change the way students learn, practice, and get help in math? And what kinds of tools or approaches do you think will be most important as math education continues to evolve?

Series Solutions of ODEs in Maple Followup

senthooran — Sun, 21 Jun 2026 11:39:05 Z

Little bit of a followup on the "Series Solutions of ODEs in Maple" online seminar.

According to Mathematical Methods for Physicists, 7th Edition by Arfken, Weber and Harris,

Pages 343-345,

Singular points are classified as regular or irregular

Irregular points are called essential singularies.

They show how to apply these to famous differential equations in Quantum Mechanics and other physical applications (examples given in Farlow's Partial Differential Equations for Scientists and Engineers).

In Section 12.1 of Mathematical Methods for Physicists, the complex series Laurent expansion (chapter 11 of the book) is applied to generalized to the complex plane (see Saff and Snider Fundamentals of Complex Analysis for Mathematics, Science and Engineering, 2nd Edition). Not too sure how Maple handles contour integrals though.

It seems that a regular point is the same as a ordinary point, as per Elementary Differential Equations and Boundary Value Problems, 8th Edition by Boyce and DiPrima, Chapter 5.

Animating a Polyhedron

pchin — Tue, 09 Jun 2026 13:32:04 Z

A little while ago, I created a video, Engaging and Enlightening Students with Maple Visualizations, that showed a sample of Maple visualizations that would be helpful in teaching math. Doing that allowed me to get reacquainted with some of Maple's plotting features that I hadn't used for a while. As a result, I made a second instructional video for my Maple tips series, Animating a Polyhedron in Maple.

I chose this topic because I thought it would show several features in Maple that might not be known to all users. I list them below and encourage you to try them out.

The plots:-polyhedraplot command allows you to create a 3-D plot of a polyhedron, including one of 138 polyhedra that Maple knows about.
The list of named polyhedra available can be obtained by calling the plots:-polyhedra_supported command.
The viewpoint option, which allows you to create an animation by varying the viewpoint through a 3D plot, can be used to rotate the polyhedron.
Finally, the Export feature allows you to save the plot animation as an animated GIF.