[b]An Ancient Greek Challenge[/b]
The study of Geometry was born in Ancient Greece, where mathematics was thought to be embedded in everything from music to art to governing the universe. Plato, an ancient philosopher and teacher had the statement, “Let no man ignorant of geometry enter here,” placed at the entrance of his school. This illustrates the importance of studying shapes and logic during that era. Everyone who learned geometry was challenged to construct geometric objects using two simple tools known as Euclidean tools:
● A straight edge without any markings (back of a ruler or paint stick)
● A compass
The straight edge could be used to construct lines, and the compass to construct circles. As geometry grew in popularity, math students and mathematicians challenged each other to create constructions using only these two tools.
Some constructions were reasonably easy (Can you construct a square?), some more challenging (Can you construct a regular pentagon?), and some impossible even for the
greatest geometers (Can you trisect an angle? In other words, can you divide an angle into three equal angles?). Archimedes (287-212 B.C.E.) came close to solving the trisection
problem, but his solution used a marked straight edge.
Today, you will use GeoGebra compass and straightedge tools to explore geometric constructions as in the time of Euclid.
[i]adapted from GaDOE Geometry CC Learning Plan: Challenges From Ancient Greece[/i]
