Ball Is Life

Week 3: Symmetric Matrices

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DIBS: Symmetry in basketball (equipment/ball)

“I will never look at a (traditional) NBA basketball the same again” – This is just right after researching for this post. *amazed meme* *my whole life has been a lie meme*

Ever since 7 years old, I thought basketball looks like this.

expectation

Little did I know, it is just like a tennis ball or baseball traditionally made by joining two complementary (symmetric) pieces.

deconstructed baseball

In basketball, what you should see from one side is different from what you have on the other. Below’s a photo of the different flows of the leather patches in the front and rear view.

leather patches

So the first animation (gif) should be…

reality (on most, if not all traditional basketball)

Each leather patch embraces the other. Here’s an animation.

animation

 

Here’s a real life example. Observe the 2 leather patches carefully. (sorry for the low resolution ‘.gif’, here’s the link for the video source: youtu.be/DQc8miHqdqQ?t=2m20s )

NBA basketball (Spalding brand)

Basketballs have two planes of reflective symmetry, as do tennis balls. But these balls also have a 2-fold rotational symmetry. A cube has nine planes of mirror symmetry, while some soccer balls have fifteen!^[2]

sources:
[1] https://blender.stackexchange.com/questions/41298/asymmetrical-basketball  (visited on May 21, 2017).
[2] John Horton Conway. The Symmetries of Things, p. 12
[3] https://math.stackexchange.com/questions/688749/number-of-reflection-symmetries-of-a-basketball (visited on May 21, 2017).