The Mathematical Reason Why Manholes are Round

Have you ever wondered why manholes are circular?

The answer is simple. Using other shapes, it is possible for manhole covers to fall through the hole. For example, a square cover with side length 1 meter can fall through a square manhole even if the lip (stopper) makes the side length of the manhole  less than that of its cover.

To explain further, suppose a 5-cm lip is placed on each side of the hole, then that leaves a square hole with side length 90 cm.  Using the Pythagorean theorem, that hole has diagonal of more than 1.27 meters, large enough to swallow the cover (see 3rd illustration in the 1st figure) with a burp.

man-hole

On the other hand, the constant diameter of a circular cover ensures that it  does not fall through the circular hole no matter how roughshod (I hope I used the word correctly) it is moved by vehicles.  » Read more

Ted Talk: Robert Lang on the Mathematics and Magic of Origami

In the previous post, I have shared to you sites about origami or paper folding.  Aside from these resources, I have also posted several examples of using it in the classroom. Several of these examples are introduction to the notion of proof, and getting the square root and cube root of a number. In addition, I have also shared a video using mathematics of origami to fold  gift wraps minimizing wastage.

Rober Lang: Origami Artist

But origami is a lot more than the things you have read above. Today, the art is already used as a model for airbags and telescope in space. There is even a research for  using it in devices that will be used in heart surgery.  » Read more

The Mathematics of Christmas Wrapping

Last year, I shared to you a Christmas song titled the 12 days of Christmaths. Today, I’m going to share to you something more mathematical and a more surprising link between Christmas and mathematics: the mathematics of gift wrapping.

How do you wrap a gift with minimal wastage? Mathematician Sarah Santos has answered the question using the concept of nets and surface area in the video below.

Have a happy holidays and I hope that you have not wrap your gifts yet. Otherwise, you have to do it next year.

Merry Christmas!

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