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Transcript
```Euclidean Constructions: Beautiful, Beautiful Geometry!
Euclid’s Elements was the first text to put logic to geometry. Most of the
thirteen books of the Elements are about geometry, others are about number
theory.
The person Euclid is worth reading about, and here is the place to start. You
will find a good bibliography at the end of the article linked above.
Euclid proposed that geometric ideas were certain. Given a few basic
definitions (23), five axioms (also called postulates) and some “common
notions” about the world, he derives the rest of what is known about
geometry using the Aristotelian logic that we worked with in Math 211.
To understand Euclid we need to understand what is possible when
drawing plane figures using a straight edge and compass. For Euclid, being
able to construct geometry in this way was a proof that the geometry could
be trusted.
Many, many beautifully symmetric planar drawings are possible using
simply a straight edge and compass. You will have three of these assigned,
but may do extras for extra credit. I will only accept well-crafted work.
As you construct designs of great beauty, you will notice, as Euclid did, that certain constructions have
great beauty as well as great utility. You are responsible for knowing how to perform the individual
constructions that Euclid found most important. Open Math Reference explains and gives an animation
and often a proof for each one of these, and we will see these same proofs in section 14.3.
To the left find a photo of a crop circle.
These are reported to appear suddenly in
fields throughout the world. Some claim
that alien visitors are responsible, others
claim that this is an elaborate world-wide
hoax.
For extra credit, recreate this construction
and color it so that the light green (area
where the crop is knocked down) is one
color and the darker green is a separate
color. You may include a different color
edging as this researcher has done. Be
prepared to explain how you thought