Curriculum

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======Notes on Euclid Elements======

[[http://farside.ph.utexas.edu/Books/Euclid/Elements.pdf|Euclid pdf]] in Greek and English

David Joyce, Clark University: 
[[https://mathcs.clarku.edu/~djoyce/elements/elements.html|Eudlid html]] with Commentary

geogebra.org: [[https://www.geogebra.org/calculator|
Drawing Tool]] simulating compass and straight-edge\\

====Notes====

lab/scripts
  * i2d.py
  * ispiral.py
  * liner.html

curriculum python scripts
  * example_sinewave_interactive.py
  * helix3.py - renamed
  * ispiral.py
  * test3ddraw.py

khan academy - vector dot product and vector length \\
khan academy - matric vector products \\
khan academhy - vectors and spaces - defining the angle between vectors \\
ikhan academy - electric motors - the dot product \\

Gil Strang lecture 1: The column space of A contains all vectors Ax


tibetan buddhist chant\\
https://www.youtube.com/watch?v=iei5QA_aPp8 \\

Projects
  * Beauty patterns
  * Model sk8 actuators
  * Linear arithmetic algebraic geometric exponential logarithmic 
  * Patterns earthquakes 
  * String ball not tangle tangled knot skein 
  * Normal Pareto

Mauy in Phuket 
https://www.thephuketnews.com/mauy-the-graffiti-artist-spraying-a-wall-near-you-73183.php

Street Art in Chiang Mai
http://www.hipthailand.net/variety/art-design/624
 

Chomsky\\
The capacity for language and for mathematics did not come about through natural selection.
https://youtu.be/1X-AkJZUIiE 


Explanation of complex numbers
https://youtu.be/ALc8CBYOfkw 

Tesla battery plant in India
https://www.scmp.com/news/asia/south-asia/article/3123802/india-promises-tesla-lowest-production-costs-will-persuade

Sapolsky: three brains: reptilian, limbic, neo cortex
https://youtu.be/hg6XUYWj-pk 


George Carlin: sociology: individuals versus groups
https://youtu.be/Y2NjUKOw1Qg 


Chomsky on merge function
  * Combine two objects into bigger one
  * Example of language used as thought
https://youtu.be/9JScy7ulDpE 

Looking for a variation of multi-armed archemides spiral
https://math.stackexchange.com/questions/3718071/looking-for-a-variation-of-multi-armed-archemides-spiral

Who benefits from these beliefs?

If language has not evolved, per Chomsky, can the same be said for all aspects of human behavior?

====Contents====

^ Book ^ Title ^ Definitions^ Propositions^
|   1 | Fundamentals of Plane Geometry Involving Straight-Lines    |  23|   48|
|   2 | Fundamentals of Geometric Algebra                          |   2|   14|
|   3 | Fundamentals of Plane Geometry Involving Circles           |  11|   37|
|   4 | Construction of Rectilinear Figures In and Around Circles  |   7|   16|
|   5 | Proportion                                                 |  18|   25|
|   6 | Similar Figures                                            |   4|   33|
|   7 | Elementary Number Theory                                   |  22|   39|
|   8 | Continued Proportion                                       |   0|   27|
|   9 | Applications of Number Theory                              |   0|   36|
|  10 | Incommensurable Magnitudes                                 |  16|  115|
|  11 | Elementary Stereometry (Solid Geometry)                    |  28|   39|
|  12 | Proportional Stereometry (Measurement)                     |   0|   18|
|  13 | The Platonic Solids (Regular Solids)                       |   0|   18|
|     |                                                            |  131|  465|

Each proposition describes how to draw a geometric shape 
using only a straight-edge and a compass,

proving equality and inequality of lines and angles, 
without explicit measurement of either.

Each proposition builds on the ones before.

And therefore, each proposition is an axiom.



====Book 1.  Plane geometry.====  
2D shapes that lie in a single plane.  Polygons.\\
point, line, plane, surface\\
angle: acute, obtuse, perpendicular\\
boundary, figure: circle, rectilinear\\
circle, center, semicircle\\
rectilinear figures: trilateral, quadrilateral, multilateral\\
trilateral: equilateral, isosceles, scalene, right-angled, obtuse-angled, acute-angled\\
quadrilateral: square, oblong, rhombus, rhomboid, trapezia\\
parallel lines (infinite)\\

{{ :euclid_propi1.gif?300|}}
Proposition 1.1.  How to construct an equilateral triangle. 
  * Draw the base of the triangle as a line segment $\overline{AB}$.  
  * Use a compass to draw a circle with center $A$ and radius $B-A$.
  * Draw a second such circle with center $B$.
  * Take the point $C$ where the two circles intersect.
  * The triangle $ABC$ is equilateral.

Proposition 1.2.  How to draw two line segments of equal length.

Proposition 1.3.  Same as 1.2, alternate method.

Proposition 1.4  A proof that two triangles with two sides and the intervening angle equal,
are equal triangles.

Proposition 1.5  A proof that in an isosceles triangle, the two angles at the base 
are equal.

Proposition 1.6  A proof that in a triangle having two angles equal, 
the opposite sides will be equal also.

Proposition 1.7  A proof that for any three points, there is only one triangle.

Proposition 1.8  

Proposition 47.  A proof of the Pythagorean theorem.

====Book 2. Geometric algebra.====  
10 of the 14 propositions can be restated algebraically.
quadratic equations.

Proposition 1.  The distributive property of multiplication over addition.

\begin{align}
x(y_1+y_2+\cdots+y_n) = xy_1+xy_2+\cdots+x y_n\\
\end{align}

Euclid did not use the word "distributive", nor did he use this equation.\\
He told the story in terms of lines and rectangles. \\
x is the length of a line.  xy is the area of a rectangle.\\

Proposition 2. Same as prop 1, but only using 1 cut, two rectangles.

\begin{align}
x(y_1+y_2) = xy_1+xy_2\\
\end{align}

Proposition 3. 

\begin{align}
x = y + z \iff xy = y_2 + yz\\
\end{align}