Geometry and Volume --- Formulas Beyond Pi
Geometry was born as a useful tool for land measurements and lately for surveying. We probably would go back to Mesopotamia and around the Tigris River, 3,500 years ago. Little by little became what is today, especially when Euclid started to build a rigorous Science from his axioms and postulates and made his ELEMENTS, the Bible for Geometry way up until the nineteenth Century. The basic formulas that you already saw in school are represented on the graph to the right.
The three first formulas are easy to understand and keep in our memory. But lets help the kids that are new to Geometry.
axb means a multiplied by b
axa means a times a, or a squared
h which originated from the word 'height'
PI
Pi is a constant quotient that relates a circumference with its diameter; no matter how big the circle is, the diameter will increase accordingly.
The area of a circle is a result of this relationship
A=πr2,
Later, when you take calculus you will find how mathematicians came out with that formula.
ELLIPSE
If you notice an ellipse has two radius which define his oval shape. As you can see, its formula
is simple and good resemblance of an area of a circle.
VOLUME FORMULAS
If you see a CYLINDER, you can notice that is the result of adding infinitesimal circles. Remember that volume is a 'quantity' of three-dimensional space. So we will need units that resemble that space. From cm3 to m3we will find this units all over these formulas, same situation with cubic feet or cubic inches.
CYLINDER
A=πr2 H
H represent the height needed to add a third dimension to our circle area. Back in times of our first merchants, there was a need to keep track of volume. Wine, milk, beer, even grains of all kind, needed the knowledge or notion of volume.
SPHERE
The volume of an sphere might be hard to memorize but was very useful for our first astronomers from Babylonians, to Mayans to Renaissance.
V=(4/3)π r3
How to use mnemonics on this formula
Imagine both of your hands. Now left hand shows four fingers. Right hand show only three. Try playing the fitting game by interlacing your three fingers into your four left fingers. Now comes the last part: Let your sister or brother put a picture of Gordy the pig on your interlaced fingers and try to hit an stereo Cubic radio that she/ he is holding against you. Easier than this? Maybe but, now you cana see how your brain is saying geez! Mr. Cross!
ELLIPSOID
(4/3) pi r1 r2 r3
Makes sense right? You are giving an egg and they want you to find its Volume. You will need those three R's (r1,r2,r3) that define its unique volume. We still have the 4 fingers over 3 and with Gordy's picture still bothering you( pi=3.141592)
