Studio of Engaging Math

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Source: Noetic Learning

✈️ Why Do Airplane Routes Look Curved? ✈️

Look at a flight map and you might notice something strange: the shortest route between two cities often looks curved.

Why wouldn’t a plane simply fly in a straight line?

Because Earth isn’t flat.

On a globe, the shortest path between two points is part of a great circle - a circle whose center is the center of the Earth. What looks like a curve on a flat map can actually be the closest thing to a straight line on the surface of a sphere.

That’s why a flight from New York to Tokyo, for example, can appear to bend dramatically northward on a typical flat map.

This is a beautiful example of geometry changing the way we see the world: the route hasn’t suddenly become longer because it looks curved. The map has changed how we see a path on a three-dimensional surface.

Real flights also take weather, air traffic, restricted airspace, and other factors into account, so airlines don’t always follow the exact mathematical shortest path.

Math isn’t just about calculating distances. Sometimes it explains why the world looks the way it does.

💥 Fun Friday for Parents 💥

A small pan can hold only two slices of bread at a time.

Each side of a slice takes 30 seconds to toast.

How can you toast both sides of three slices in just 90 seconds?

📚 MATH BOOKSHELF 📚

Can bad drawings make you better at math?

Ben Orlin’s Math with Bad Drawings makes a convincing case that they can.

The book explores mathematical ideas through humor, everyday situations, puzzles, probability, statistics, geometry, and, as promised, deliberately terrible drawings. But the drawings aren’t just decoration. They help strip away the intimidating language that often makes mathematics feel more complicated than it really is.

Orlin’s approach is playful, but the mathematics isn’t shallow. Behind the jokes are questions about how we reason, why our intuition sometimes fails us, and how mathematical thinking can reveal patterns we might otherwise miss.

Perhaps the best thing about the book is who it’s written for: not only people who already enjoy math, but also readers who are convinced they don’t.

That idea feels very familiar at Studio of Engaging Math. Mathematics doesn’t become engaging by making it less intelligent. Sometimes it simply needs to be approached from a different angle.

And occasionally, with a really bad drawing.

THE MINISTRY OF MATH PRESENTS
THE PROBLEM OF THE MONTH

Attention, witches, wizards, Muggles, and mathematically gifted house-elves!
A most troubling situation has arisen at the Ministry of Math:
Our pancakes are taking far too long to cook.
Our owls are flying themselves dizzy.
One of our bags of coins appears to have been tampered with.
And every night, a gang of house-elves is running through the Ministry opening and closing 1,000 doors.

Naturally, someone suggested using magic. Absolutely not.
The Ministry has strict rules against using spells when a perfectly good mathematical solution exists.

So we are calling upon the cleverest young minds at the Studio to help us.
Each month, the Ministry will release several problems, from Level 1 for our younger problem-solvers to Level 4 for those brave enough to challenge even their parents.
Choose your level. Or ignore the recommendations and try all who dare!
You may use paper. You may use pencils.
You may draw pictures, make tables, experiment, argue with your family, or stare dramatically into the distance until inspiration strikes.

Wands, however, must remain firmly in their cases.
Solutions may be submitted by owl, by email, or in the Studio drop box.
Good luck.
The Ministry of Math is counting on you.
P.S. Ten points to your house (grade) for a particularly clever solution.

📚 MATH BOOKSHELF 📚

How Not to Be Wrong - Jordan Ellenberg

What if math isn’t really about getting the right answer, but about learning how not to reach the wrong one?

In How Not to Be Wrong: The Power of Mathematical Thinking, mathematician Jordan Ellenberg takes mathematics far beyond equations and textbooks. He explores how mathematical thinking can help us make sense of statistics, probability, polls, lotteries, risk, patterns, and everyday decisions.

One of the book’s most compelling ideas is simple: math is a way of seeing structure where we might otherwise see only information.

Numbers can be technically correct and still lead us to misleading conclusions. A percentage can sound impressive without telling us much. An average can hide what is really happening. A seemingly unlikely coincidence may actually be quite probable. Ellenberg shows why asking the right mathematical questions matters just as much as knowing how to calculate.

And you don’t need to be a mathematician to enjoy the book. It was written for a broad audience, using real-world examples to introduce surprisingly powerful ideas without turning the experience into a textbook.

That’s also why it belongs on the Studio bookshelf: we want students to see mathematics not simply as a school subject, but as a tool for thinking, questioning, and understanding the world more clearly.

Studio verdict: A great read for curious adults, parents, older students and anyone who has ever wondered, “When am I actually going to use math?”

Why Do Bees Build Hexagons? 🍯🐝

Take a close look at a honeycomb and you’ll find one of nature’s most elegant geometry lessons.

To store honey efficiently, bees need cells that fit together with no empty spaces. Equilateral triangles, squares, and regular hexagons can all tile a flat surface perfectly, but but hexagons have a special advantage.

For the same amount of storage space, a hexagonal pattern requires less total wall material than comparable triangular or square patterns.

For bees, that matters. Building honeycomb requires wax, and producing wax costs energy. The geometry of the hexagon allows a colony to create a strong, space-efficient structure while using material efficiently.

This mathematical idea is so interesting that the optimality of the hexagonal arrangement became known as the Honeycomb Conjecture and mathematician Thomas Hales finally proved it in 1999.

Sometimes the best geometry lesson isn’t on a whiteboard. It’s inside a beehive.

💥 Fun Friday for Parents 💥

A little challenge for your Friday brain.

Each letter represents a different digit from 0 to 9. The same letter always represents the same digit, and no number begins with zero.

There’s only one solution. Can you find it?

Even variables have boundaries.

Math can be logical, precise, and still make us laugh. Sometimes all it takes is looking at a familiar algebra phrase from a slightly different angle.

That’s our kind of math.