Archimedes :: The Man Behind The Legend
September 20, 2008
Imagine being brought into the world at a time when Alexander the Great has just conquered Egypt. He dies and is replaced by King Ptolemy I who establishes the Library at Alexandria – the first intellectual Mecca to EVER be established in the history of mankind. This same King hires Euclid to compile all of the known mathematics in the world, which has recently been published. You are born to an astronomer anyway, and at the age of 4 you are sent from Syracuse to this great city of knowledge, Alexandria, to study for twelve years under many teachers, not the least of whom may have been Euclid himself! While you are there you get to see the Pyramids, Sphinx, the annual flooding of the Nile, the irrigation canals, and ALL of the splendor that was the height of, arguably, the greatest civilization to ever inhabit the Earth. He would have seen all of the mechanics of the wine and olive presses, the methods of leverage used by the Egyptians to construct such monumental pyramids, and learned all of the other royal subjects of philosophy, astronomy, and logic. [Read more]
Wait, wait, wait … 1=2?
September 14, 2008
Yes, it’s true*! Through a few simple laws of Algebraic Rule we can now make this claim with 100% confidence**! How you ask? It is all quite simple:
Assumption #1: The first concept you have to understand is the Identity Property, which states that any number is equal to itself.
As an example: 15=15, 33=33, and 101=101. That doesn’t seem so difficult does it? Thus, let us claim that any two integers , x and y, are equivalent in value when: x=y, where x is equal to y (redundant, I know).
Argument :: Thus, since x = y:
Step 1.) Multiply both sides by x: x*x = x*y
Step 2.) Subtract y*y from both sides: x*x – y*y = x*y – y*y
Step 3.) Factor both sides: (x+y)(x-y) = y(x-y)
Step 4.) Divide out the common factor, (x-y), on both sides:
(x+x) = x
2x = x
Step 6.) Divide both sides by x:
Whoa! We are left with 2 = 1
But wait, there’s more! If 2 = 1 then I can multiply both sides by 2 and get 4 = 2 … but if 1 = 2 and 2 = 4, then 1 also equals 4!!! In fact, I can effectively claim that every number equals every other number!
Next time you are at the store, by demonstrating your superior mathematical ability, you should be able to pay $1 for absolutely anything since 1 equals any amount they could be asking for (don’t feel offended if this doesn’t actually happen).
Or…you can check out this video on The Four Rules of Algebra that explains where we might have gone wrong. (Note: You must be logged in to your free account to watch the video tutorials. Don’t have an account yet? Sign up here.)
