Math Dodger Game

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Using numbers, number operators, and math functions.

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Numeric values: 0, 1, 2, 6.7, 10.083…

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Just numbers by themselves. Sometimes these are called numeric literals.

Integers: whole numbers

Floating point: numbers with a fractional part

Numbers can have their fractional part too. The decimal point is between the digits of the number.But, floating point numbers have the decimal point at any spot between digits, like: 3.14159 or 651.75.

Arithmetic binary operation (+, -, *, /)

The operations for basic arithmetic: add, subtract, multiply, and divide.

Remainder (%)

This is a extra operator for division. You can find out how much is left over if one number doesn’tdivide into the other number evenly.

We know that 4 / 2 = 2, so 2 divides into 4 evenly. But, 5 / 2 = 2 with a remainder of 1. So, theremainder operation, 5 % 2 = 1, gives the number that’s left over from a division operation.

Exponent (**)

The exponent operator will multiply the number on the left by itself for the amount of times of the number on its right. That is, 4 ** 2 = 4 * 4 and 2 ** 3 = 2 * 2 * 2. The area of a square that has sides with a length of 5 is equal to one side multiplied by another. For a square, all sides are equal, so:

But using the exponent operator, this is the same as:

The volume of a cube is three sides multiplied together. The two volumes are the same:

Square root

The square root of a number is another number that when multiplied by itself it becomes the original number. You know that 2 * 2 equals 4 so the square root of 4 is 2. It’s called a square root because the area of a square is the length of two equal sides multiplied together. The root is the length of a side.

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Absolute value

When you want to know how much a number is without its sign (+/-). The absolute value of -5 is 5 and the absolute value of 5 is also 5. The absolute value is sometimes called the magnitude.

Minimum and maximum of two values

You can get the smaller or the bigger of two numbers with the min() and max() functions.

The minimum of 2 and 9: Math.min(2, 9) equals 2.
The maximum of 3 and 9: Math.max(3, 9) equals 9.

Round

If a number has a fractional part, you can make the number change to be the closest, next integer value. This is called rounding. Rounding the number 6.78 will make it be 7 and rounding 9.3 will give you 9. If a number has a fractional part greater than or equal to 0.5, the number will round up to the next whole integer value with the higher value. Otherwise, it will round down to the next lowest integer value.

For negative numbers, they round toward the absolute value (the absolute value of -8 is 8) of the number. So, -5.23 rounds to -5 and -2.68 rounds to -3.

Ceiling

To make a number change to the next higher whole number (integer), get the number’s ceiling value. The ceiling value for 1.234 is 2 since that is the next higher whole number. For the negative number of -3.63, its ceiling is -3 since that’s the next higher whole number.

Floor

To make a number change to the next lower whole number (integer), get the number’s floor value. The floor value for 8.76 is 8 since that is the next lower whole number. For the negative number of 6.17, its floor is -7 since that’s the next lower whole number.

Truncate

The fractional part of a number is removed by truncating it. If a number has the value 54.234 its truncated value is 54. Truncation works the same way for a negative number. The truncated value of -34.913 is -34.

Random value

Make up any number from a minimum value to a some maximum value. If you want a random number up to100, say: Math.randomRange(0, 100).

Trigonometry

Functions for finding numbers of angles, sides of triangles, and positions on a circle. These functions are also used to make information for wave signals.

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What’s your angle? Degrees or radians

A compass shows where North is and the direction to it is 0 degrees (which is also 360 degrees). If you walk directly to the East, then your direction will be 90 degrees on the compass. This isalso the measurement of the angle between the path of your direction and the path to North. If pointyourself to North and spin around to the right (clockwise) in one spot, you will see the compass change from 0 degrees, go up to 359 degrees, and back to 0 degrees. So, a full rotation is 360 degrees, or fullcircle.

Another way to measure angles is to use numbers that are special to the size of circles. A circle has two important numbers related to it. They are called the radius and pi. The radius is the distance from the center of the circle to its outside edge. A long time ago, people learned that no matter how biga circle is, if you divide the length of its outside edge by the length of its radius, you always get the same number back. They decided to call this number pi. It’s 2 times pi actually, because they used the whole length across the circle which is two lengths of the radius.

Now, we don’t have to worry about the radius anymore, we can just use some part of 2pi to tell where any spot on the edge of a circle is. Any part or all of 2pi is called radians. We can use radians to measure an angle of direction too, just like with the compass. Except now, we spin 2pi radians around the circle instead of 360 degrees.

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What number is pi?

As it turns out, pi is an irrational number. That means it has a fractional part that uses more digits than we can display. So, it’s best to use a constant in code for the value of pi. In case you’re curious, the first 32 digits of pi are: 3.1415926535897932384626433832795.

Luckily, you can use the built-in constant Math.PI.

In code, you use radians for angle measures. All of the math functions for trigonometry use radians.

Changing degrees to radians

What’s 60 degrees in radians? Well, one radian is (2 * Math.PI / 360) radians. Or, to make itsimple, (Math.PI / 180) radians. So, 60 degrees is (60 * Math.PI / 180) radians.

Sine

Get the length of the vertical (up or down) side of a right triangle at some angle. But, thesine value is the length of the vertical side divided by the length of the longest side,its hypotenuse.

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What’s the sine of 60 degrees? Math.sin(60 * Math.PI / 180) equals 0.5. The vertical side of a right triangleis one half the length of the longest side when the opposite angle is 60 degrees.

Cosine

Get the length of the horizontal (left or right) side of a right triangle at some angle. But, thecosine value is the length of the horizontal side divided by the length of the longest side,its hypotenuse.

What’s the cosine of 45 degrees? Math.cos(45 * Math.PI / 180) equals 0.707. The length of the horizontal sideof a right triangle is about 70 percent of the length of the longest side when the angle between themis 45 degrees.

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