Astrology:
”it began in wonder”
Starts, yearly calendar, and navigation. Back then the stars were very visible. And we can see about 6000 stars with the naked eyes.
It was useful for measuring and remembering the tides.
It seemed that the stars had self-motion, which would make it seem that they were alive, or at least somehow animated. The star signs, the constellations were important.
There was an idea that there was a connection between the heavens and the soul.
7 was very important.
For Pythagoeans, everything in nature followed patterns that can be expressed in terms of whole numbers, and fractions of whole numbers.
It seems the five platonic solids are the only regular polyhedra.
This was shown in class using a proof by cases.
This was influential all the way past Kepler. Kepler was very into astrology and numerology.
If we go further back, about 20000 years ago, there seems to still have been awareness of mathematics. eg. the Ishango bone which had 168 lines carved on 3 sides of it. Though we do not really know why, but there seems to have been principles to it.
It seems the babylonians had already discovered pythagorean triplets. However they didn’t prove it nor did they formalise this understanding, though they had awareness of that kind of knowledge.
Geometry, the measurement of the earth.
One context in which this direct translation makes sense is in terms of Egyptian agriculture.
Each year the lands were flooded, so it was impossible to keep track of who owned what land, so this had to be remeasured each year, by ropestretchers, in order to measure out what each individual was due in terms of land mass to perform agriculture on.
With rudimentary tools like a rope, you can easily create a right angle, using for example knots and a rope.
Numbers that were not a ratio of whole numbers were not numbers at all to the pythagoreans.
Euclid made an important proof of for the pythagorean theorem, the ”windmill” proof. We are supposed to go through this proof at home by ourselves.
If we have a triangle with the hypotenus equaling the diameter of a circle, and the third pointing being any random point on the circle, it will always be a right-angled triangle; Thales’ theorem.
Dido, was allowed to mark her territory on a given part of the mediterranena sea, based on how many ox hides she could encompass an area into. She made the ox-hide into cords and covered an area based on