Archive

Posts Tagged ‘mathematics’

IgNobel Prize Winners!

September 29, 2011 Leave a comment

Well, the IgNobel Prizes wrapped up not too long ago. Scicurious was live blogging the event and there was also a live webcast.

And the winners are:

A group from Europe won the Physiology award for demonstrating that yawns are not contagious in Red-Footed tortoises.

A group from Japan won the award for Chemistry by demonstrating the ideal amount ofwasabi to put in the air in order to wake people up. The purpose? A wasabi fire-alarm!

A couple of studies demonstrating how people make decisions when they really, really have to pee won the award for Medicine.

A group from Oslo won the Psychology prize for studying why people sigh. 

The Literature prize was given to John Perry of Stanford University for his theory of “Structured Procrastination“.

The Biology prize was given to a couple guys hailing from Canada, Australia and the USA for discovering a type of beetle that mates with stubby beer bottles.

A bunch of loons (e.g. Harold Camping) won the Mathematics prize for predicting the world would end and being wrong.

The Peace prize was awarded to Arturas Zuokas, the mayor of Vilnius, Lithuania, for driving over an illegally parked luxury car with an armored tank.

The Public Safety prize was given to John Senders of the University of Toronto for conducting a driving safety study by having someone drive down the highway and have avisor repeatedly hit them in the face.

And finally, (and most importantly!) the Physics prize was given to a group from France and the Netherlands for studying why discus throwers get dizzy, but hammer throwers don’t. Very important with the 2012 Olympics coming up!

______________________________________________________________________

REMINDER: This blog is moving! The new location is http://www.aquantumofknowledge.com/ 

The new RSS Feed is: http://feeds.feedburner.com/AQuantumOfKnowledge

Remember to update your subscriptions! This site will no longer be supported after September 30, 2011. 

Thanks! 

Ryan

Advertisements

Happy Pi Day Everyone!

March 14, 2011 Leave a comment

Yes March 14 (3/14) is indeed pi day; a day to celebrate everyone’s favourite irrational number.

As a special treat for you, I’m going to show you a way to calculate pi to a high accuracy for yourself (knowledge of a computer programming language helps).

So the number pi is closely related to the geometry of the circle. The area of a circle is represented by the following formula:



Where r is the radius of the circle. So we can use this relationship to calculate pi, but we can do it without measuring anything! Instead, we are going to use something called a “Monte Carlo” simulation

Monte Carlo simulations are very useful in physics. They use random numbers to simulate a real-world system. Since they are based on random numbers, the technique is named after the famous Monte Carlo casino.

Ok, so imagine you have a square that is 1 meter by 1 meter. Now imagine you place one-quarter of a circle with a radius of 1 meter over top of this square, like so:

Since the radius of the circle is 1 meter, and we are looking at exactly one-fourth of the complete circle, the area of this “slice” of circle is:

The area of the square is

And since it is 1 meter in length and 1 meter in width, the area is simply 1 meter squared:

Since the area of the square is simply 1, the ratio of the area of the square to the area of the slice is:

So we can see that pi is directly related to the ratio of the area of the slice to the area of the square.

Don’t worry, I’m goin’ somewhere with this…

Now comes the Monte Carlo part of the problem. We are going to generate 2 random numbers between 0 and 1. The first random number will be an x-coordinate, and the second will be a y-coordinate. For illustrative purposes, lets say the numbers turned out to be 0.5 and 0.5. So lets put a red circle at (0.5, 0.5):

We can see that this point lies inside the circle. In fact, any x and y values which satisfy this equation:

will lie inside the circle.

So what if we generated a huge number of points and counted the number that landed inside the circle? If we did this, then the ratio of the number of points which landed inside to circle to the total number of points would be:

Which you see is exactly the same as the equation above which related the area of the slice to the area of the square, except for one little difference. The “squiggly line” equal sign in the above equation means “approximately equal to”. It indicates that this method is an approximation because we are only using a finite number of points. If we generated an infinite number of points, that “approximately equal” sign will change to a regular equal sign.

So now all we have to do is run this calculation for a large number of points (N) and we will find that:

So how accurate is this method? Well again it will depend on the number of points. For example, if I run this method using 10 points I get a value for π of about 3.6.

If I use N = 100 points I get π ~ 3.16

And if I use N = 1 000 000, I get π = 3.140916

which is getting pretty close to the actual value of about 3.1415926539…

There you go. I’m sure your life will be much richer and meaningful now that you have this information. Now if you’ll excuse me, I’m going to eat some pie.

Math Can Be Cool. No, Seriously!

January 25, 2011 1 comment

I did physics in University, and I had to take math courses. I hated the math courses.

And I like to make jokes at my friends who did Applied Math or Pure Math as their degrees, because I just found it so boring.

But dammit if this isn’t the coolest thing I’ve seen all day:

Notice it starts with the Fibonacci Sequence, makes a Fibonacci spiral, and from there it just keeps going.

Awesome.

Who Is Better At Math, Guys or Girls? Answer Found Within…

October 15, 2010 1 comment

It’s always been an unfair stereotype that girls are not as good as guys at math. A lot of girls feel like they are not supposed to be good at math; that math and science are boys territory.

Science teachers and parents have been trying to spread the word that its OK for girls to be good at math, and to like math. And now, we have the science to prove it.

A recent meta-analysis of the published research in this area was performed. In total over 1.2 million people were studied between 1990 and 2007. Students from grade school through college level were included, as well as the results from several long-term, large-scale studies. The results all show that there is no significant difference between the math skills of men and women.

JS Hyde, one of the authors on the paper, discussed why there is still a stereotype in our society,

There is lots of evidence that what we call ‘stereotype threat’ can hold women back in math. If, before a test, you imply that the women should expect to do a little worse than the men, that hurts performance. It’s a self-fulfilling prophecy.

So having the data to show that women are just as good at math as men is only half the battle. We have to start making a change in our culture and encourage more girls to pursue their interests in science and math.