By calculating a very simple integral we can see that π ≠ 22/7 regardless to what we were told in school.
I constantly have students coming into my college classes and trying to interchange between π and 22/7. Let’s be clear, 22/7 is a relatively good approximation for π (it is correct to 2 decimal places) but it certainly is not equal to π. I want to show you an integral I like to get my class to calculate at the end of an ``Introduction To Calculus Course” to exemplify the fact that these numbers are not equal. …
Would you still take an IQ test if you knew what they have been used for?
In this article, I want to talk to you about some of the dark histories behind IQ tests that I certainly wasn’t aware of until recently. I have always had a problem with IQ tests, in my opinion using an IQ test to determine someone’s intelligence is equivalent to using a bank balance to determine someone’s happiness, but doing some research really opened my eyes to just how dangerous the use of IQ tests has been in the past, and the damage they are still causing.
It all began in France
In 1882, the French government passed a law stating that all children had to…
In this article, I want to show you an incredible little trick for calculating cos, sin, and tan of five basic angles using just your hands. Which hand, well that's up to you, but I'll focus on using my left hand. Warning: This article contains a very bad drawing of a hand, for this, I do apologize!
Ok, so let’s begin. I want you to hold your left hand in front of you so that you are looking at your palm. I next want you to label your five fingers, starting from your pinky finger, as 0°, 30°, 45°, 60°, and 90°. Great, so you should now have the following image in mind:
How does this help us calculate the sine or cos of our five basic angles? Well, let’s start with sin. To calculate the sine of one of these five angles we apply the following formula:
I had a very clever school teacher who knew, if you want to get kids to practice their arithmetic without complaining then the easiest thing to do is to create a game out of it. I in no way claim this particular teacher created any of these games herself, but they certainly worked. In fact, they worked so well that to this day, if I am on a bus or a train, or just waiting around for something in general, my mind still wanders back to trying to figure some of these out.
The best part of these games, at…
Over 2300 years ago, Euclid gathered together some fascinating results which still lie at the heart of Number Theory today. Among these, we can look at one in particular which allows us to easily determine when solutions exist to problems involving powers.
Suppose you begin with the number 8. Now consider different powers of 8:
8¹=8, 8²=64, 8³=512, ... and so on.
If you were asked to find a power of 8 so that the resulting number ends in a 4, then this is easy. We can see from out list that 8²=64. Similarly for a power of 8 so that the resulting number ends in a 2, 8³=512. What about a power of 8 so that the resulting number ends in a 0? Well this time we don't have an answer immediately from our list, so what should we do? …
A fantastically simple calculation of π.
Buffon’s needle Problem, which was first posed in 1777 by its namesake Georges-Louis Leclerc, Comte de Buffon, is a fantastically simple problem which allows us to calculate, or at least approximate, the value of π through a simple experiment. It can be stated in many different formulations, but we will consider the following one:
Suppose a needle of length L is dropped onto a piece of paper which has been lined with evenly spaced parallel lines. What is the probability of that the needle will cross one of these lines?
At first glance it may seem that such a simple…
StephenwithaPhD
Mathematics enthusiast trying his hand at writing.
