**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.**

- The Super Special Function
- The Quasi-Sequence
- Rhymes in Math
- Trigonometry Tricks
- Diameters in Terms of Radii
- Matching Matrices
- Matrix Magic
- Average Antics
- Factorial Fractions
- Complex Numbers Meet the Pythagorean Theorem
- Consecutive Integer Addition
- Squaring Square Matrices
- Delightful Division
- Nifty Number Nine & Its Multiples
- The Formula for the Circumference of a Spiral
- Unit Fraction Uniqueness
- Super Summation
- The Formula for the Sum of Consecutive Integers From 1 to
*x* - Delightful Division 2: Number of Nines in a Divisor
- Trigonometry Tricks 2
- Trigonometry Tricks 3
- Trigonometry Tricks 4
- Dividing Numbers With Consecutive Digits
- Magic Cut
- Flipping Digits
- Roman Numeral Twist
- Pythagorean Power: Exponential Excellence
- Super Summation 2
- Unit Fraction Uniqueness 2
- Consecutive Integer Multiplication
- Trigonometry Tricks 5
- Trigonometry Tricks 6
- A Shortcut for Multiplying by 25
- Mega Matrix Multiplication
- Heavenly Half-Percentages
- Cuckoo For Conjugates!
- Mega Matrix Multiplication 2
- Cubing Square Matrices
- Consecutive Digit Slide
- Fraction Frantics
- Using All 4 Aritmetic Operations on the Same Number
- The Square Roots of Cubes
- When Square Roots & Absolute Value Match!
- Super Summation 3
- The Digits in Halves of Even Numbers
- Super Subtraction
- Logic Checkers
- Multiplication Vs. Division By Zero
- The Not-So-Naughty Not!
- Powerful Patterns: Square Roots
- Delightful Division 3: Reciprocals of Half-Integers
- Root Repetition
- Digit Cloning With Multiplication!
- Number Sandwiches
- Super Subtraction 2: The Formula for the Difference of Consecutive Integers From 1 to x
- Single Simple Statements Can Create Tautologies!
- Square Root Squabble
- The Staircase of Falsity
- Complex Number Kookiness!
- Powerful Patterns 2: The Negative Powers of 5
- Super Summation 4
- Super Summation 5
- Unit Fraction Uniqueness 3
- Super Summation 6
- Complex Number Kookiness 2: Adding Integers to the Imaginary Unit!
- Rad Radicals!
- Adding 2 Powers of 1 Half
- The Staircase of Truth
- Square Root Squabble 2
- Tricky Transposition!
- Super Summation 7
- Tricky Transposition 2!

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)

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:

(* x* is also equal to the number of rows & columns!)

The 1st formula is in ** geometric series** form, the 2nd one is in

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

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 *sexaginti-* means "60"; 3 × 60 + 3 = 183.

Note: The number you pick for the variable ** x** must be a

Here's the **inverse** of the *-illion* function!

X = (log(Y) - 3)/3

P.S.: About dividing by **3** in the **inverse** of the *-illion* function:

If the remainer in the quotient is

**1**, then**Y**=**ten "X"-illion.**If the remainer in the quotient is

**2**, then**Y**=**hundred "X"-illion.**If there's no remainer in the quotient, then

**Y**=**"X"-illion.**

For example, the **googol** is a 1 followed by **100 zeroes**, so according to the **inverse** of the *-illion* function, it's also **10 dotrigintillion** since the prefix *dotriginti-* means "32" & (log 10^{100} - 3)/3 = (100 - 3)/3 = 97 ÷ 3 = 32 + 1/3; the remainer is **1** in this case.

Here's a bonus fact about imaginary/complex numbers:

P.S.: If * x* is a negative number, then it's -

Here's a bonus fact about triangles:

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:

Another bonus fact!

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:

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:

log_{x}Y ÷ log_{x}Z = log_{z}Y; none of the 3 variables are equal to **zero!** Neither X nor Z equals **1.**

Here's a bonus fact about trigonometry:

tan X = (sin X)/(cos X) = (sec X)/(csc X) = 1/(cot X)

cot X = (cos X)/(sin X) = (csc X)/(sec X) = 1/(tan X)

That's right! These are the classic Tangent & Cotangent Formulae! They both work with secants & cosecants, too! For more details, see the math tricks about trigonometry.

Here's another bonus fact about imaginary/complex numbers:

(If neither **a** nor **b** are negative, considering **a + b i**)

(1 + *i*)^{2} = 2*i*; angle(1 + *i*) = 45°, so angle(2*i*) = 90° and 45 × 2 = 90

Here's another bonus fact about logarithms:

(log_{x}Y)^{-1} = log_{Y}X; neither X nor Y equals **1 or 0.**

Yet another bonus fact about logarithms:

log_{10^X}(10^{Y}) = Y/X; X ≠ 0

Note: You can substitute **10** with another number & get the same fraction! (But don't pick **0 or 1**)

Here's another bonus fact:

(3*i*)^{2} ≠ 3*i*^{2}; (3*i*)^{2} = -9 & 3*i*^{2} = -3

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

© Derek Cumberbatch