* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download Euclidean Constructions: Beautiful, Beautiful Geometry! Euclid`s
Document related concepts
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 through your construction.