The Loop Game: Pool in Elliptical Table

Mathematics enthusiast and author Allex Bellos has created an elliptical pool table and he named it “The Loop Game.” It was supposed to always make the ball go to the table pocket. This can be done by placing the pocket at one of the foci and hitting the ball placed on the other focus. This is easy to say theoretically, but of course in playing, you also have to consider Physics.

Watch the video of one of the newest interesting games that uses mathematics in real life.

To those who are interested about ellipse, he has an explanation about in his book “The Grapes of Math: How Life Reflects Numbers and Numbers Reflect Life.”

You can find the website of the game here and watch extra footage in Youtube here.

What is the horizontal line test?

In January of this year, we have discussed about the vertical line test. We have learned that if a vertical line intersect a graph more than once, then that graph is not a function. In this post, we learn about the horizontal line test and its relation to inverse functions.

Suppose we have a function f. Then, we input x and call the output f(x). If we do things backward, suppose we have the number y which is in the range of f. What value should we input to f to get y? Let’s have a more specific example.

Suppose we have the function f(x) = x^2. And we choose the number y = 9 which is in the range of f. What number should we input in f to get 9? Well, we will have two numbers, those are 3 and -3. Continue reading

Banach-Tarski Paradox and A Great Discussion About Infinity

This video is a rich discussion about about infinity. It starts from the famous infinite chocolate problem, countable infinity, uncountable infinity, Cantor’s diagonalization system, Hilbert’s hotel, and the Banach-Tarski Paradox. Although the last part is a bit too much for the level of this blog, the explanations before it of the concepts before it are extremely clear and helpful.

I had several discussions about infinity in this blog particularly the content of Counting the Real Numbers, The Grand Hotel Paradox, and One to One Correspondence. You might want to check them out.

3 Free Whiteboard Software for Mac Users

If you are a Mac user, and if you want to use a whiteboard software in your class or if you want to screencast your lectures, then you can choose among the three whiteboard software below. The first two are free and the third one has a free version.

3 Free Whiteboard Software for Mac Users

1. Paintbrush

Not many people use it, but Paint for Mac is a very useful software. It is a Mac equivalent Paint in Windows. I was using Paint before I migrated to Mac and I’m still using it often particularly in simple image editing particularly cropping. Paint can also be used as a whiteboard software. I myself have used it many times.  Continue reading

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