Axelodo 2.0
Math for Smarty Pants

Home
La La Land | Games Galore | Interesting Links | Don't Contact Me | Monkeyland | World Events | Tennis Tutor | Academia | Math for Smarty Pants | Book and Movie Reviews | My Writing or Artwork | Editorials | Ask the Authors | Archives

I'm pretty sure most of you don't come to this web site to do math, but you may find some of this interesting. Especially if you really like to learn new things. On this page, I'm going to put bunches of crazy math tricks and formulas for those times when you're tired of doing boring calculation.

Divisibility Rules
 
First, let's do basics - how you can tell if a number is divisible by some common numbers.
 
2 - Obviously, if the number in question ends in a 2, 4, 6, 8, or 0, then it is a multiple of two.
 
3 - If the digits of a number add up to a multiple of three, then it is a multiple of three; e. g. 729 =>  7+2+9=18, 18 is a multiple of 3 so 729 is a multiple of 3.
 
4 - Just look at the last two digits (NOT the sum); if the two digit number is a multiple of four, so is the whole number. "00" is a multiple of 4. e.g. 564738294857456: only look at the last two digits. "56" is a multiple of four, so the whole number is also.
 
5 - Another obvious one - if the number ends in 5 or 0, then it is a multiple of 5.
 
6 - If the number is a multiple of 2 AND 3 (see above), then it is a multiple of six.
 
7 - This one's a little bit tricky - sometimes it may even be easier to just divide. Take the last digit and multiply it by 2. Then subtract the result from the other digits. Continue this process until you get to the first digit. If the answer at the end is a multiple of 7, the original number is also a multiple of seven. This trick isn't really very helpful, but what the heck.
 
8 - This is similar to the trick for 4; if the three digit number formed by the last three digits of a number is a mutiple of 8, then so is the whole number.
 
9 - This is similar to the trick for 3; when the sum of all of the digits of a number is a multiple of nine. But there is also something special about this one: if it is not a multiple of nine, the remainder when the sum of the digits is nine is also the remainder when the whole number is divided by nine.
 
10 - Obviously, if the last digit of a number is 0, then it is a mutiple of ten.
 
11 - Take the first digit of the number in question, subtract the second, add the third, subtract the fourth, add the fifth, and so on, and if the result of the equation is a multiple of 11, then the whole number is, too. REMEMBER: 0 is a multiple of 11.

Sumations

Euclidean Geometry
 
What is Euclidean geometry? What is geometry? Well, most of you should know that geometry is the study of the relations, properties, and measurement of solids, surfaces, lines, and angles. Confused? Basically, it's the study of shapes and what make up the shapes. Euclid was a Greek who first studied shapes and came up with several ideas that you may find obvious called postulates.
 
First you need to know some basic terminology, or nomenclature (impress your friends with that word).
 
Point - undefined, 0 dimensional, a dot
Line - undefined, 1 dimensional (width), infinite in two directions, see postulates below
Line segment - The part of a line between two points
Ray - A line that ends in a point on one side (only infinite in one direction)
Plane - undefined, 2 dimensional (length and width), infinite in all directions, flat surface
Angles - two rays
Parallel - two lines that never intersect are parallel to each other
Transversal - a line that crosses two or more other lines
Perpendicular - two intersecting lines that form four right angles
 
 
If you want to find any postulates or theorems about any of these things, just use the "Find" tool (Ctrl+F) and type in the words you want to look for.
 
I would say that 70% of all geometry is using postulates and theorems. So here they are.
NOTE: The symbol "<" stands for angle, since I can't make a real angle symbol on the computer.
 
Postulates
Postulates are facts that cannot be proven, but are known to be true. Most of these are very obvious, but again, there is no way to prove them.
 
Ruler Postulate - The points on a line can be paired with real numbers so that for any two points P and Q, P corresponds to zero, and Q corresponds to a positive number.
 
Segment Addition Postulate - If Q is between P and R, PQ+OR=PR
 
Protractor Postulate - If you have a ray, you can choose any number between 0 and 180 and draw exactly one other ray on either side of the first one to form an angle.
 
Angle Addition Postulate - Rays AB and BC form an angle. If there is a point D that is in between these two rays, then <ABD + <DBC = <ABC.
 
Here are some more basic postulates: (collinear means on the same line, and noncollinear means not on the same line). It is important to note that points, lines, and planes CANNOT be defined, only described.
 
Through any two points there is exactly one line.
A line contains at least 2 points.
Though any three noncollinear points there is exactly one plane.
A plane contains at least 3 noncollinear points.
If two points lie on a plane, the entire line that has the two points is on the plane.
If two planes intersect, their intersection is a line.
 
Perpendicular and Parallel Line Postulates:
 
Corresponding Angle Postulate - If two parallel lines are cut by a transversal
 
Here are some postulates dealing