It was a long time in the history of mankind before it occurred to anyone that mathematics is useful or even necessary to science and nature. However, now math can explain more, in a smaller and less complicated statement, than words.

Mathematics is an absolute necessity in physics. Almost everything in physics ties back to mathematics, even the creation of any form of life. In this section, the basics of mathematics in physics will be described. Also, if able, graphics will show these mathematics in action.

What will be shown: Very Basics, Gravity, Test Your Skills, Fractals

Before you study physics you will need to be familiar with some basic algebra. In this section, we will review important math techniques. Don't let numbers and calculations intimidate you. This section will help you become more familiar with math in general and in physics.

Units

The universal system for measuring matter is the metric system. Unfortunately, there are many different types of measurements in the metric system so in order to learn this we highly recommend looking at this image. Click Here. If you do not know what some of this is, move on to Scientific Notation and learn about it a little more.

Scientific Notation

Ok, so the form for scientific notation can get a bit confusing. First, start with a variable. We will call it X. X can be any number. Then take a positive integer and use it to replace variable N. The formula is X*10^N. Take the next part and add it to the equation. Study this and try the problem at the bottom of this part of the section. This information should also help you to understand the previous section better.

Velocity and Acceleration

Look around, you will find that almost everything is in motion. We will analyze the motions and think about how fast and how far the object moves.

Distance and displacement are different. When you travel 50 km to the East and then 20 km to the West, the total distance you traveled is 70 km, but your displacement is 30 km East.

In physics, we say that distance is a scalar and displacement is a vector. A scalar has a magnitude and a vector has both a magnitude and a direction. A scalar is one dimensional and a vector is two dimensional.

The formula is:
Velocity = Displacement / Elapsed Time

Newton's law of gravity defines the attractive force between all objects that possess mass. Understanding the law of gravity, one of the fundamental forces of physics, offers profound insights into the way our universe functions.

The famous story that Newton came up with the idea for the law of gravity by having an apple fall on his head is not true, although he did begin thinking about the issue on his mother's farm when he saw an apple fall from a tree. He wondered if the same force at work on the apple was also at work on the moon. If so, why did the apple fall to the Earth and not the moon?

We are telling you this merely to show you the questions that were in his mentality at the time.

Newton eventually came to the conclusion that, in fact, the apple and the moon were influenced by the same force. He named that force gravitation (or gravity) after the Latin word gravitas which literally translates into "heaviness" or "weight."

You may be wondering how all of this relates to math. Well, instead of telling you the way gravity works in english we will give you the equation:

Let us break this formula down:

• F_g = The force of gravity (typically in newtons)
• G = The gravitational constant, which adds the proper level of proportionality to the equation. The value of G is 6.67259 x 10^-11 N * m² / kg², although the value will change if other units are being used.
• m₁ & m₂ = The masses of the two particles (typically in kilograms)
• r = The straight-line distance between the two particles (typically in meters)

We know this seems complicated. Just practice the equation it will eventually get easier.

One of the most complex mathematics sections in physics is fractal studies. We know that we said that this was a basic mathematic / physics section; however, we figured that we show how complicated math in physics can get.

Fractals are complicated, but they are appealing to the eye. One of the most famous fractals is the Mandelbrot Set. We will show you this later in the lesson.

But what is a fractal, you ask? A fractal is generally a rough or fragmented geometric shape that can be split into parts, each of which is (at least approximately) a reduced-size copy of the whole. The phrase was coined by Benoit Mandelbrot.

This has to do with physics and math. Firstly, it is related to math because the shape is a complex math problem. It relates to physics because fractals can help us understand the universe as well as life and how things exist. Some fractals that are made as math problems can be found as the shapes of galaxy or even fruit. Anything we see can be a fractal.

So, you want to see the math? It may confuse you if you are not farmilliar to calculus. That is the full formula for the Mandelbrot Set. If you wish to see the actual fractal made into a functioning java applet here.

Again we are showing this not to confuuse you but simply show that every single thing is related to mathematics when it comes to physics.