Googol and Google

In last week’s post, we have talked about large numbers and their importance to scientific studies and everyday life. In this post, we talk about one of the most famous large numbers: googol.

A googol is the name of the number which is 10^{100} or a 1 followed by one hundred zeros. If you are wondering how large it is, well it is fairly large since the number of atoms in the observable universe is only 10^{80}. That means that we need 10^{20} universes, the size of the observable universe, to create a universe with googol number of atoms.

googol

The term googol was coined in 1938 by Milton Sirrota (he was 9 years old the time he invented the term), nephew of Edward Kasner, an American mathematician. Kasner was famous for his book Mathematics and the Imagination where he introduced the term googol. » Read more

Guest Post: Derivatives and an Introduction To Calculus

by Shaun Klassen

One of the mathematics subjects most feared by students is the “dreaded” differential calculus subject.  Absolutely, it is more complicated than more common basic algebra that most would have studied up to this point.  And of course, to work with calculus, one must be familiar with all of the earlier concepts that build up a strong mathematical foundation, including things like algebra, trigonometry, and graphing.  However, this is not to say that calculus has to be hard, or “impossible.”  It is completely doable if you start slowly by learning the general problem solving strategies.  In this guest post, I want to introduce the main concept of differential calculus – the derivative – and I encourage you to visit my math website to find out much more information about this subject.

The name “differential calculus” is a descriptive one – it is based on differences, or changes.  More specifically, it is all about describing how one quantity changes with respect to another one, or in other words, the rate of change.  The derivative is used to express this function, but let’s examine this concept a little more closely by considering everyone’s favourite rate of change: velocity.  » Read more

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

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