The post What’s the point in math? appeared first on Class Coach Tutoring.

]]>While technically true I suppose, this is quite the wrong way of looking at it. You don’t really *need* any subject to get through life. What’s the point in knowing history if it won’t pay your bills? Why write a report that wont get you laid? Why learn chemistry when you don’t handle chemicals in your daily life?

But they’re all important. And math, incredibly so. Math is more than mere number crunching. Math has so many applications, and is the foundation for understanding our universe.

**Advancement in science –**Without math, where would we be? Your smartphone wouldn’t exist. You wouldn’t be able to read this fantastic blog. We wouldn’t have technology of any sort. Science relies on mathematical formulas and understanding. It goes beyond technology, to practically every scientific advancement we have ever made. If you are in any way interested in science, I strongly urge you to practice math. It makes foundation for science, and you’ll hardly get anywhere without it.**Art, too! –**Math is used all the time in art. One of the most obvious examples is proportions, knowing how things work as they get bigger or smaller. This is used to create perspective in drawings, and can make them look more realistic. It’s also constantly used in graphic design, as geometric designs are usually more aesthetically appealing. I make abstract art as a hobby (also sometimes known as “doodles”), and it’s all based off of geometry. For some fantastic examples of this, check out Vihart on YouTube. She is the internet’s math doodling expert.**Understanding our world**— If you’ve taken a calculus course, you understand the complexities involved in understanding just one simple concept: motion. The derivative is incredibly important in understanding the way things move. This ties in again with my previous point, because some of the simplest concepts in physics rely on the derivative. Another favorite concept of mine is the Fibonacci sequence. Fibonacci numbers occur weirdly often in nature. You can find them on butterflies, pine cones snails, and even humans. These numbers might even be worthy of another blog post!**Logical capabilities –**Math is a skill. Many people see it as memorizing formulas or crunching numbers, but it is so much more than that. When you think mathematically, you think logically. Many people don’t know how to think logically, and this is one of the many problems in the world. Logic really should be taught as part of the standard curriculum to young children. But I digress – math teaches you to think about things in a straightforward manner. This brings me to my next point:**Problem solving –**Math, as I said before, is a skill. Understanding math is more than just formulas. When you truly understand a theory, you won’t have to memorize the formulas – you’ll be able to derive them for yourself. The distributive property is a very simple example of this. 3(x+4), if you know the distributive property, equals 3x+12. The three is multiplied by both the x and the 4. But if you don’t know the distributive property, you can still figure it out! With integers, multiplication is repeated addition. Therefore, 3(x+4) equals (x+4)+(x+4)+(x+4), or, rewritten, x+x+x+4+4+4, which equals 3x+12.

Math shows you how to think differently. This, I think, is the most important reason to learn it. Logic and problem solving are incredibly important throughout all of life. Even if you never use calculus or algebra again, once you’ve learned it your mind has been enriched, and you will be better off for your efforts. Don’t focus on memorizing the facts, but instead on the reasons behind them. Math is about understanding how things work. Whether you’re doing a Sudoku puzzle, designing a computer program, or building a bookcase, understanding how to think logically about your situation will always be a benefit.

The post What’s the point in math? appeared first on Class Coach Tutoring.

]]>The post The Pythagorean Theorem appeared first on Class Coach Tutoring.

]]>Today is a special day. You see, today marks the very first day of the rest of my life. In order to mark this special occasion, I am starting a blog. This blog post will forever be remembered (or forgotten) as the first among many.

I have decided to dive right into things, and begin with one of my favorite mathematical formulas. This formula is incredibly useful, the concept is simple, and it is easy to remember. It is known as the Pythagorean Theorem.

The Pythagorean theorem is a formula which directly relates to right triangles. A right triangle is composed of a 90 degree angle, also known as a square angle, and two smaller angles. The theorem gives a relation for each of the three sides. Using the formula, if you know the length of two sides of the triangle, you can find the length of the third side.

Generally, the two sides which form the right angle are assigned the variables A and B, and the side opposite the right angle is assigned the variable C (look at the picture for a good visualization). The formula states that A squared plus B squared equals C squared.

Although named for Pythagoras, the Pythagorean theorem’s history is debated. In all likelihood, Pythagoras was not actually the first to discover this property, nor the first to write about it. Some historians believe the Babylonians may have known about the theorem, accounts of the Pythagorean Theorem in India may go as far back as 8000 BC.

The methods of proof for the theorem are numerous and vary widely. A great number of these are simple geometric proofs, and require nothing but some algebra and geometry to understand. If you’re interested, there is a long list of them at Wolfram MathWorld.

The theorem comes up surprisingly often in higher math. You’ll see it all the time, especially in calculus and physics. One of the most common usages of it arises in vectors. A vector is merely a direction and a magnitude, usually visualized as an arrow or a line.

In the diagram below, you can see two vectors, A and B. When you put them end-to-end, they add to vector C. Each vector is composed of two components, one vertical and one horizontal component. If you add the horizontal length of A to the horizontal length of B you obtain the horizontal length of C, and the same applies to the vertical lengths. When you have the horizontal and vertical lengths of C, you simply plug them into the Pythagorean theorem to find the length of vector C. Thus, 15^{2}+9^{2}=C^{2}. Solving (with a calculator) gives C=17.5. It’s a surprisingly simple process, with an immense number of applications.

The post The Pythagorean Theorem appeared first on Class Coach Tutoring.

]]>