A lot of students from Palos Verdes and Peninsula High School come into our Redondo office despising math, and I don’t blame them. Mathematics is a tough subject that takes a lot of time to understand, and students often try to get by by memorizing the rules, proofs, and theorems without ever perceiving how they work. After all, it’s a nasty subject that I’ll never really need. Who cares about the directrix of a parabola? When do I need to know how to calculate the area of a n-sided polygon? What’s the point of being able to do basic arithmetic in my head? I can just use my iPhone calculator to get the answer, or Google search it. That’s good enough.

It’s tough to argue against these points, but I believe that putting your best foot forward when tackling math builds a solid foundation, not only in regards to academics but to life as well. If a child is willing to put in the time to genuinely understand how trigonometric identities work, they’ll be more likely to work for things in life, whether it be a job, sport, or relationship in the future. If a student understands that they need to address their poor grades in math head-on instead of ignoring it, they won’t run when life gets tough. On the other hand, if that student resorts to taking short cuts in math or gives up after trying only once, they’re likely to throw their hands up in the air whenever they face adversity. Just like there are no short cuts to becoming a great Sea King or Panther athlete, there are no short cuts in academics, especially math.

So please, help your child develop good life habits by spending some extra time one or two nights a week helping them with their math. Make sure they show their work and don’t just guess the answer. Ask them questions to see how well they really grasp the material. Tell them, “Good job!” or “Nice work!” when they’re trying their best. Teach them the joy of hard work. As a math tutor, there are no secrets to help these students. I help them first understand the basics and then build on those basics. I teach them how to systematically analyze a problem and try various approaches instead of looking in the back of the book for the answer. I encourage them to ask questions when they don’t understand something. These are all good habits that people need to succeed in life, and mathematics is a great place for children to start developing them.

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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