Tuesday, March 9
Projects : Do you have an approved project with partners?
Do you have a plane on how you'll use the time of the break for your project?
Kieval Lecture
"The
Mysterious Arithmetic of Knots"
on Thursday Evening- 7:30 pm FH 118 by John Conway
You can get knot models by clicking on a picture in the
Knot Zoo or by using a
simple knot viewer (randomly chosen).
.... From John Conway (et al.) 's web materials on Geometry and The Imagination
A mathematical knot is a knotted loop.
For example,
you might take an extension
cord from a drawer and plug one end into the other: this makes
a mathematical knot.
It might or might not be possible to unknot
it without unplugging the cord. A knot which can be unknotted is
called an unknot.
Two knots are
considered equivalent if it is possible to rearrange one to
the form of the other, without cutting the loop and without
allowing it to pass through itself.
The reason for using loops of string in the mathematical
definition is that knots in a length of string can always
be undone, so any two lengths of string are
equivalent in this sense.
If you drop a knotted loop of string on a table, it crosses over
itself in a certain number of places. Possibly, there are ways to rearrange
it with fewer crossings--the minimum possible number of crossings
is the crossing number of the knot.
Figure 5:
This is drawing of a knot with 7
crossings. Is it possible to rearrange it to have fewer crossings?
 |
Make drawings and use short lengths of string to investigate the following
problems.
- 1.
- Are there any knots with one or two crossings? Why?
- 2.
- How many inequivalent knots are there with three crossings?
- 3.
- How many knots are there with four crossings?
- 4.
- How many knots can you find with five crossings?
- 5.
- How many knots can you find with six crossings?
Continuing with Similarity.
Show more of FAPP Similarity Video
Similarity and Editing- font size applications.
Wingeometry similarity.
Rubber band activity.
Arithmetic and Geometric Series.
Adding ...
Application to economics.
Begin: Seeing the infinite... small and large.
How many points are there on a line segment? Can you count them all?
Start Space filling curves.