We were inspired by a post on Twitter by Olivier Longuet shown below. The object in the photo is an icosahedron, a 20-sided 3D shape, made out of three golden rectangles with side lengths that obey the golden ratio (1:1.618033…). To make a cardboard version of the icosahedron, print out this document and follow the instructions! You can also make

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## Take and Make: Transform Square to Triangle, and Square to Hexagon

These are cardstock designs, so if you laser cut the pieces they will all stay attached to each other. SVG of Cardstock versions Square to Triangle Square to Hexagon SVG of straight cut lines (square/hexagon is a the parallelogram) And if you are interested, here’s how you make the pieces. Triangle to Square: This transformation was made based on Ernest

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## Take and Make: Angle Sum Set

This is a fantastic way to layout this problem posted on twitter by Olivier Longuet and pointed out to me by Ralph Pantozzi. The drawing progression is on the right or you can etch the left (blank) onto wood, and add the finished pieces as you figure it out. Our files are here if you want a jpg, svg, Corel

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## Take and Make: Moscow Puzzles Crayfish and Flower

Here are two fun puzzles you can find in this classic book. The files to make them are right here! (secret: The wood is colored with Bingo stampers) Moscow Flower and Crayfish, Laser cut file types: Corel 2020, Adobe Illustrated, SVG, JPG

## Take and Make: Making a Pool Test Apparatus

You don’t need robots and computers, just a system and apparatus to organize the steps! This model is based on the results alluded too but not completely explained by an Israeli company in the recent NY Times article by David Halbfinger on creative pool testing options. https://www.nytimes.com/2020/08/21/health/fast-coronavirus-testing-israel.html Trying to come up with one of these is a great activity for

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## Take and Make: Parallel Ruler and Compass Rose

In 2019, we brought our suite of Navigation Math to New York to share how we relate math to Texas History and the voyage of La Belle which is on exhibit at the Texas State History Museum. Files to make our version of the Parallel Ruler are here. Files to make our version of the Compass Rose are here. Participants

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## Take and Make: Genaille-Lucas Rulers

Genaille-Lucas Rulers are pretty cool. They are a clever calculator that you can use to multiply some pretty big numbers. MathHappens summer staff member Anh Nguyen made a colorful jumbo set from scratch in Corel Draw that you can download and print — its in 3 pages but be careful of the sizing or use the one page below: Page

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## Take and Make: Proof without Words Sum of Odd Numbers – Freese Transformation

This Geometric Transformation shows how the sum of the first 6 consecutive odd numbers is the square of 6, or 36. It’s the classic “proof without words”. Freese’s Transformation also shows this relationship, but his “squares” have sides sqrt 1, sqrt 3, sqrt 5, and so on. Freese Corel File, Adobe Illustrator File, Jpg printable

## Take and Make: Experimental Mathematics Cucumber Edition

Here’s a fun one! Inspired by a conversation with Chris Daniels of Public Math. He said roll paper around a cylinder and cut on an angle to get an ellipse and produce a sine wave. So we did! And you can too. Then you can make a roller from ellipses, reflect your sine curve and roll the elliptical roller along

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## Take and Make: Freese Transformation 178

This design is from a lost manuscript of Ernest Irving Freese found by Greg Frederickson and published in his 2018 book “Ernest Irving Freese’s Geometric Transformations: The Man, the Manuscript, the Magnificent Dissections” Frederickson mentions Freese’s manuscript in the bibliography of his 1997 book, “Dissections: Plane & Fancy, and included selections from it in a 5-part series of short chapters spread

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