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.

This section is divided into quarters. Which one do you want to view?


Please select a trick to view:

  1. The Super Special Function
  2. The Quasi-Sequence
  3. Rhymes in Math
  4. Trigonometry Tricks
  5. Diameters in Terms of Radii
  6. Matching Matrices
  7. Matrix Magic
  8. Average Antics
  9. Factorial Fractions
  10. Complex Numbers Meet the Pythagorean Theorem
  11. Consecutive Integer Addition
  12. Squaring Square Matrices
  13. Delightful Division
  14. Nifty Number Nine & Its Multiples
  15. The Formula for the Circumference of a Spiral
  16. Unit Fraction Uniqueness
  17. Super Summation
  18. The Formula for the Sum of Consecutive Integers From 1 to x
  19. Delightful Division 2: Number of Nines in a Divisor
  20. Trigonometry Tricks 2
  21. Trigonometry Tricks 3
  22. Trigonometry Tricks 4
  23. Dividing Numbers With Consecutive Digits
  24. Magic Cut
  25. Flipping Digits
  26. Roman Numeral Twist
  27. Pythagorean Power: Exponential Excellence
  28. Super Summation 2
  29. Unit Fraction Uniqueness 2
  30. Consecutive Integer Multiplication
  31. Trigonometry Tricks 5
  32. Trigonometry Tricks 6
  33. A Shortcut for Multiplying by 25
  34. Mega Matrix Multiplication
  35. Heavenly Half-Percentages
  36. Cuckoo For Conjugates!
  37. Mega Matrix Multiplication 2
  38. Cubing Square Matrices
  39. Consecutive Digit Slide
  40. Fraction Frantics
  41. Using All 4 Aritmetic Operations on the Same Number
  42. The Square Roots of Cubes
  43. When Square Roots & Absolute Value Match!
  44. Super Summation 3
  45. The Digits in Halves of Even Numbers
  46. Super Subtraction
  47. Logic Checkers
  48. Multiplication Vs. Division By Zero
  49. The Not-So-Naughty Not!
  50. Powerful Patterns: Square Roots
  51. Delightful Division 3: Reciprocals of Half-Integers
  52. Root Repetition
  53. Digit Cloning With Multiplication! NEW!
  54. Number Sandwiches NEW!
  55. Super Subtraction 2: The Formula for the Difference of Consecutive Integers From 1 to x NEW!

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!

2+2 = 2*2 = 2^2 = 4


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:

If n = the number of rows & columns of a checkerboard, then the total number of squares is equal to:

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!)

which is the same as:

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 a bonus fact about imaginary/complex numbers:

The absolute value of a complex number (x + xi) is equal to x times the square root of 2, if x is greater than or equal to 0.

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 even, then your age will be even in even-numbered years & odd in odd-numbered years!

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!

The Mathematics of Pac-Man™:

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!)

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

© Derek Cumberbatch