Hey it’s Professor Dave, let’s learn about
geometry.
If you could go back and visit any time in
the history of mankind, which would it be?
The roaring twenties?
The Renaissance?
Those are some pretty good ones, no doubt,
but my pick would definitely be Ancient Greece.
This civilization produced some of the most
astounding leaps of intellect in the history
of our species.
In this era, early society truly evolved into
a form that held the triumphs of the mind
in highest regard, and as a result, the Greeks
revolutionized philosophy, government, and
you guessed it, mathematics.
While there were many important figures in
these fields, some of the best work in math
was done by a fellow named Pythagoras.
His work influenced great thinkers like Plato,
and therefore all of Western civilization.
This early branch of mathematics, now called
geometry, was derived largely from drawing
pictures in the sand, and it is one of the
oldest topics in math.
Great thinkers would draw shapes like circles,
rectangles, and triangles, and try to understand
the characteristics of these perfect forms.
In this way, mathematics came to be defined
as the field of inquiry in which all questions
have completely objective answers.
The sum of two angles, the ratio of side lengths
on a triangle, these are values that can be
firmly arrived at and are completely inarguable,
just like the solutions of polynomials that
we studied in basic algebra.
This kind of certainty was impossible in the
crude physical world, the mysterious subject
of natural philosophy.
Mathematics was revered as the study of divine
perfection in physical form, and Pythagoras
even had a little bit of a club surrounding
his beliefs about numbers.
Or, we can go ahead and say it, it was a cult.
But a nice, math cult.
Its members were called Pythagoreans, and
among their doctrines was a healthy dash of
mysticism for good measure.
Some of it turned out to be nonsense of course,
like their belief that the orbits of celestial
bodies must obey perfect numerical ratios,
just like the consonant musical intervals.
As it turned out, this space symphony, as
romantic as it sounds, is not real.
The planets are distributed about the solar
system more or less at random, just like every
other planetary system we can see in our galaxy.
But their contributions to math have stuck
around, and between the work of Pythagoras
and other great mathematicians like Euclid,
mankind’s ability to describe the universe
was dramatically transformed.
This change was so profound, in fact, that
the geometry we learn in high school today
is not very different from the geometry of
this ancient time.
So let’s move forward and learn all about
the shapes and angles and axioms that comprise
the topic of geometry.
