Johann Carl Friedrich Gauss (1777 –1855) had an exceptional influence in many fields of mathematics and science and ranks among history's most influential mathematicians. In the last chapter of the Disquisitiones, Gauss gives his proof for the construction of regular polygons with straightedge and compass. The construction is possible, if the number of its sides is the product of distinct Fermat primes and a power of 2.
COMPASS CONSTRUCTIONS
How many centres does a triangle have?
Key questions
Can we use a pair of compasses accurately?
Can we construct an angle bisector?
Can we construct a perpendicular bisector?
What are loci?
Can we use ICT effectively?
5 lessons
Specification detail
Literacy
stories that set a frame or background
stories that accompany or intertwine
stories that introduce
stories that explain
stories that ask a question
stories that entertain
The Number Devil by Hans Magnus Enzensburger
Wantzel
Introduce..
using compasses - 1
crop circles - 1
where should I stand - 2, 3
angle bisector - 4
Develop..
grid loci - 2, 3, 4
loci and regions - 2, 3, 4
constructing angles - 1, 2, 3
odd one out - 2, 3
three points - 3, 4
Extend...
dodecahedron inside an icosahedron - 1, 2, 3
loci ocr - 2, 3, 4
constructing regular polygons - 1, 2, 3
more advanced constructions - 1, 2, 3
squirty - 1, 2, 3
the tethered goat - 1, 4