Many people think math is really boring. This is because, for the most part, teachers are lame and don’t make the material interesting. There is a lot of cool and weird mathematics out there that kids unfortunately are not exposed to. Here are a couple of interesting mathematical oddities that will hopefully spark some interest in math:

You want to find the sum of the infinite series 1-1+1-1+1-1+1-… This pattern repeats forever. At first glance, you would likely say (1-1)+(1-1)+(1-1)+… = 0+0+0+0+… and conclude the sum is 0. At second glance you may say the 1+(-1+1) +(-1+1) +(-1+1) +(-1+1) = 1+0+0+0+0+… = 1. Turns out both of these are wrong and the sum turns out to be ½. Here is why:

Let’s call the sum of the series S, whatever it may be. So, S = 1-1+1-1+1-1+1-…

Now, look at 1-S. We get 1-S = 1- [1-1+1-1+1-1+1-…] = 1-1+1-1+1-1+1-… = S. This is the same as our original series. We just showed that 1-S = S which means that 1=2S or that S=1/2. Pretty crazy that you can add 1 and -1 infinitely many times to get ½.

Here is another cool little proof why 1=2:

Let a =b. Then a2 = ab.

So, a2+ a2 = a2+ab or 2a2 = a2+ab.

Now, Subtract 2ab from both sides of the equation. Doing so, we get:

2a2 -2ab= a2+ab-2ab

So, 2a2 -2ab= a2-ab

Now, we factor out a 2 from the left side of the equation which leave us with:

2(a2+ab) = a2+ab

Divide both sides by a2+ab leaves us with:

2=1.

Take a close look though. While everything seems to be right, we all know 2 does not equal 1. Can you find the erroneous step? If not, come to the Study Hut and we can show you what’s up.

Science most definitely should not be handled by the faint of mind. People need to understand that the difference between three-dimensional and two-dimensional is the number of axis. Any two-dimensional (2-D) object is defined by a “x” and “y” axis , where as any three-dimensional (3-D) object is defined by a “x”, “y”, and “z” axis. In simpler terms, a 2-D object has length and width, whereas a 3-D object has length, width, and height, therefore giving it volume.

Physicists believe there are anywhere from 10 to 26 physical dimensions, each discretely chosen from the patterns of atomic string vibrations. How would you explain the 10th dimension to someone? Perhaps the way to understand something abstract is through an analogy. Instead attempting to explain the concept of 10 dimensions through scientific terms, I will first attempt to explain how we relate to 2-D objects through actions in the 3rd dimension, and then relate the 3rd and 4th dimension together. I really hope that you are able follow along since I think this is one of the most fascinating physical characteristics of our world, and very few people understand the concept of multiple dimensions. Well, here we go!

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Many students find pre-calculus to be one of the most difficult courses they take in high school. At the Study Hut we work with students to help them develop a more positive outlook on the subject. We find that the reason most students struggle with pre-calculus is because they are lacking knowledge of the more basic mathematical principles. We work to get the students up to speed with basics, such as the unit circle and trigonometric functions, so that they can become successful math students.

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