Geometry and the Greeks

What did the Greeks in BC think infinity was ? The smallest thing they could see was grain of sand, therefore there must be infinite many grains of sand on the earth.

But we now have a number that is a one followed by 100 zeroes called a "google".
(yep, that is where the famous internet search engine Google got its name.)

So 10^100 = a google. That is a big number. The USA national debt in 2010 is at 14 Trillion...and that is only 14 X 10^12 or $14,000,000,000,000.

There are only 6 Billion people on this earth...or 6,000,000,000.

And only 300 Million people in the USA...or 300,000,000.

Now if 10^100 is a google, what is 10 to the google power ?

That is called a "googleplex" !! and that is the largest name number we have.

How big is it ? It is so big, we can not even image how big it is.

The smallest thing we can see (with the aid of powerful microscopes) are molecules.

We know that our Sun is a just a star. And that there are Billions of stars in our galaxy. And that there are Billions of galaxies in our universe.

A googleplex is larger than ALL the molecules in our universe !!! (that just went over my head...lol)

So how big is the number of grains of sand on the earth ? A large number or small number ? Actually it is a very small number...we estimate it to be less then 10^22...a one followed by 22 zeroes. If we were God, we could hold it in the palm or our hand (actually someone mentioned under one of God's finger nails).

So in the movie Contact with Jodi Foster, Jodi travels to another world and is met by some being...the being represents himself or herself as Jodi's dead father, and they talk while walking down the beach. The being picks up a hand full of sand, the sand falls from his palm with little sparkling stars....and i stand up and yell, YES !! (this was making a reference to the Greeks and what they thought was infinity). I love those kind of moments in my life.

What does Geometry mean ? "Geo" means earth. "Metry" means measure. Therefore Geometry means measure of the Earth.

One of the original Greek mathematicians was Thales in about 800 BC. He gave us the first five theorems or properties. One of those we have already mentioned as the Height to Shadow concept which today we say "Rise over Run" which is of course Slope (I already blogged about that in "Extra Help" and discussion about equations of lines)

But lets revisit the idea of finding the height of a tree in the woods. We have our trusty yard stick that we carry with us (3 feet long).

If we place the yardstick in the ground near the tree we can measure a 1 foot shadow. Meanwhile we can also measure the shadow of the tree, it is 10 feet.

So if we use the ratio of Height/shadow = Height/shadow, we get

3/1 = height of tree/10

Therefore the height of the tress must be 30 feet tall. (Yes, yes get your paper and pencil). Now you can measure the height of the huge electric pole by the park and the that huge building down the street.

Thales in 800 BC measure the height of the great Pyramids in Egypt. And they call him a "god" because he did NOT have to climb the pyramids to do it.

Sherlock Holmes in one of his books used this concept to find a clue that was supposedly buried at the end of a shadow, but the tree had fallen down. Watson was impressed and once again Sherlock said "elementary my boy, quite elementary".

COMMENTS:

(Am forwarding this email to all 3 sons, Manny. You taught Richard in a GRE prep class. Of course you taught Doug at Berkeley. Mike and Julee's boys go to a math and science magnet school in Ocala. I've been really impressed by what they do in math--and maybe their parents will investigate. Thanks!!)