# Some Math Tricks I Discovered

Not only will you find tricks in this section, but also some tips to help you with math, & various information about numbers, logic, & geometry. Look out for my characters here, too; they'll make this section more entertaining & educating!

Here's a bonus cartoon for visiting this section: If you can multiply big numbers with several digits quickly, then you're a super-genius! By the way, the correct answer to the math problem in the cartoon above is 5,332,114.

## Please select a trick to view:

### Note: If I discover any more math tricks, then I'll add them to this list!

Here's a bonus fact: -40 degrees Farenheit is equal to -40 degrees Celsius!

Proof: The 2 conversion functions intersect at x = -40, y = -40

F = 9/5 × C + 32

C = 5/9(F - 32)

Get a graphing calculator and see for yourself!

Another bonus fact! This is an interesting fact about the number 2, but you probably already knew it! Another bonus fact! The reciprocal of a number's square root is equal to the square root divided by the original number! (x is not equal to zero!)

Here's a fact about checkerboards! (Or you can also call them chessboards) You can calculate how many squares a checkerboard has with the 3 formulas below:

### n2 + (n - 1)2 + (n - 2)2 + ... + 32 + 22 + 12

#### which is the same as: (x is also equal to the number of rows & columns!)

### n3/3 + n2/2 + n/6

The 1st formula is in geometric series form, the 2nd one is in summation form and the 3rd is in cubic function form. Here's a bonus fact about permutations & combinations:

If you pick 2 objects at a time from any set that has at least 2 objects, the permutation-to-combination ratio is always equal to 2. In other words, there will be half as many combinations as permutations.

Here's a bonus fact about the suffix -illion:

What does the suffix mean? Well, here's the -illion function!

Y = 10^(3X + 3)

X = the prefix's number, Y = the actual number

For example, 1 sexagintillion is a 1 followed by 183 zeroes! The prefix sexagint- means "60"; 3 × 60 + 3 = 183.

Here's the inverse of the -illion function!

X = (log Y - 3)/3

Here's a bonus fact about imaginary/complex numbers: P.S.: If x is a negative number, then it's -x times the square root of 2.

Here's a bonus fact about triangles:

### Let A, B & C be the 3 angles of a triangle. Then...

sin(A + B) = sin(C)

sin(B + C) = sin(A)

sin(C + A) = sin(B)

In other words, the sine of the sum of 2 angles in a triangle will always be equal to the sine of the 3rd remaining angle!

Here's a bonus fact about birth years & age, measured in full years of course:

### If the number of your birth year is odd, then your age will be even in odd-numbered years & odd in even-numbered years!

Another bonus fact!

### After eating a power pellet...

 If Pac-Man eats 1 ghost: If Pac-Man eats 2 ghosts: If Pac-Man eats 3 ghosts: If Pac-Man eats all 4 ghosts: 1st Ghost 200 200 200 200 2nd Ghost 400 400 400 3rd Ghost 800 800 4th Ghost 1600 Sums: 200 600 1400 3000

(This is referring to the original version of the video game)

The number of points earned for each ghost refers to this summation formula: See? Even video games have math in them!

Here's a bonus fact about the Law of the Cosines: If Angle C = 90°, then the formula simplifies to the original Pyragothean theorem (since the cosine of a right angle is zero); but if Angle C = 180°, then the formula simplifies to:

c = a + b

...Because cos(180°) = -1. (That's right! Side c simply becomes the sum of Sides a & b! However, the figure would be a straight line instead of a triangle!)

Here's a bonus fact that I call my Prime Number Test:

### If an integer is not divisible by any prime numbers that are less than its square root, then it is also a prime number!

Here's a bonus fact about fractions: According to this cartoon, if the absolute value of the difference between the numerator & denominator is 1, then the fraction is already in its simplest terms! By the way, these 2 functions never intersect! Also, they're both discontinuous functions because of division by zero!

Here's a bonus fact about logarithms:

logxY ÷ logxZ = logzY; none of the 3 variables are equal to zero! Neither X nor Z equals 1.

Speaking of numbers, here are some Web pages with interesting facts about specific numbers: