## Digit Sum Game

The digit sum game is for two players, or two teams, if you want to have a team collaborate to come up with their play. Players/teams take turns picking a digit from 1-9. Once picked, a digit cannot be used … Continue reading

## Folding conic sections

Jacobs shows how to form the shape of a parabola and hyperbola by repeatedly creasing a sheet of paper with a circle, and a dot outside the circle. It works even better using a Mira. The idea is to reflect … Continue reading

## Box method for multiplying polynomials

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In algebra, most students are taught FOIL for multiplying binomials. It is an application of the distributive law of multiplication, but specifically limited to multiplying binomials. For example, What if we are multiplying more than two binomials, or polynomials that … Continue reading

## Casting out nines

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A whole number is divisible by nine if the sum of n's digits is divisible by nine. In fact, we can make the stronger statement that the remainder when we divide by 9 is the same as remainder when the … Continue reading

## Human binary computer

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As part of introducing binary arithmetic in the classroom, I use volunteers to create a human digital computer. We start with simple operations, and work our way up. Getting physically involved and watching your classmates makes it interesting, but I … Continue reading

## Mechanical sorting

I found this among the many gems in Mathematics: A Human Endeavor. The trick uses sixteen special numbered cards. Each card has a combination of holes and slots. These are used to sort the cards by inserting a paper clip … Continue reading

## Mathematics: A Human Endeavor

Harold Jacobs introduced a wonderful textbook in 1970. He updated it in 1982 and 1994. It features a blend of geometry, algebra, and discrete mathematics. His coverage is novel and engaging. Jacobs provides a thoughtful mix of discussion and problems. … Continue reading

## Divergent sums

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By time you complete high school math, you've probably encountered the idea of convergent sums, such as The idea is often presented with a story such as Zeno's paradox about Achilles and the tortoise. As the number of summed terms … Continue reading

## Numbers, big and small

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Number Two: Why not use your knowledge of the future to play the stock markets? We could make trillions. Dr. Evil: Why make a trillion when we could make... billions? The modern world presents us with numbers of unimaginable scale. … Continue reading

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Print this pdf, and cut out the four pieces. Can you arrange them into a square? How about a rectangle? What's up with that? … Continue reading

## Arrows

In the grid below, you can click or shift-click arrows. Can you fully describe what happens (or doesn't happen) when you click/shift-click an arrow? Is it possible to get all four corners pointing in different directions? Is it possible to … Continue reading

## Complete regular polygons

A regular polygon is a polygon with equal side lengths, and all vertices lie on a circle. If you have a collection of vertices, and connect all of them, you have a complete graph. So if you connect all of … Continue reading

## Super-elasticity and infinite series

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Physics problems are often greatly simplified for new students. We assume negligible friction and perfectly elastic collisions. In some problems, the assumption of negligible friction might be reasonable. But students have a harder time understanding what perfectly elastic looks like. … Continue reading