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In this sample from More Hands-on Science, we’re looking at infinitely detailed shapes known as fractals. If you do this activity, you can discover a fractal called the dragon curve!

Difficulty: Taxing Grab a calculator (or a pen and paper) Choose a three-digit number (e.g. 123) Multiply it by 7 Multiply the answer by 11 Multiply that answer by 13 You will get your starting number written out twice! (e.g. 123 123) The question is, can you work out why?

Around 3500 years ago, the Minoan people lived on the island of Crete. They had a written language, now known as Linear A, which archaeologists cannot decipher. They also had an advanced number system, which experts are finally beginning to crack!

Difficulty: Tricky We’re going to make a magic triangle! Take the numbers 1–6 and arrange them in a triangle with three numbers on each side. Swap them around until the sides all add up to the same number.

By Mike McRae Double Helix magazine is looking for your questions! Our Microscope column answers the most intriguing science, tech, engineering and maths queries you can throw at us.

Difficulty: Taxing Here’s a beautiful artwork from 1895, titled Mental calculation. In public school of S. A. Rachinsky, painted by Nikolay Bogdanov-Belsky. Can you solve the puzzle the kids are pondering? If you can’t quite see the equation, here it is:

Craft yourself a mathematical ring to learn about straight lines on donuts. Don’t laugh, they do exist!

Difficulty: Tricky Gertrude has a collection of shapes that she likes to arrange in patterns. She starts with a regular hexagon with 10 cm sides, and three regular triangles that also have 10 cm sides. She arranges the triangles around the hexagon, and then lines them up. In the end, one side of each triangle…

Difficulty: Fun I’m thinking of three numbers. They are consecutive counting numbers. When you add the first two numbers together, you get the third number. What numbers am I thinking of?

Difficulty: Tricky Ari was 10 on her last birthday, and will be 12 on her next birthday. How can this be true? Lachlan was 8 on his last birthday, and will be 12 on his next birthday. How can this be true?