- Homework, Section 4.7 (will be returned next time -- sorry!)
- Homework, Section 4.3 is due next time.
-
Activity: as a group, construct a set of platonic solids from
the paper templates.
- We can see the concept of Duality from this table.
- Two dimensional representations of Platonic Solids
- Put your eye to the face of an object and draw it.
- Is it possible to draw each objects without any edges crossing?
- Pictures of Duality
- Links: Borromean
Rings:
- "Is it possible to link three rings together in such a manner that they are indeed linked, yet if we remove any one of the rings the other two become unlinked?"
- Yes!
Standard diagram of the Borromean rings
A realization of the Borromean rings as ellipses
Coat of arms (of the municipality of Hallsberg, Sweden) showing padlocks in Borromean rings configuration
As a 13-century symbol of the trinity in Christianity
(Thanks Wikipedia!) - Activity: putting them all together: icosahedra, golden rectangles, and interlocking rings! (see page 381)
- First we make a rubber band version of the Borromean rings, using two regular rubber bands and one cut one.
- Then we use "golden rectangles" to make
both Borromean rings as well as an icosahedron,
simultaneously! Upshot:
Inside of an icosahedron one finds golden rectangles, locked together into Borromean rings....
From it, deduce the values in the following table:
| # of Vertices | Edges | Faces | faces at each vertex | sides at each face | |
| Tetrahedron | |||||
| Cube | |||||
| Octahedron | |||||
| Dodecahedron | |||||
| Icosahedron |
- Section 7.6: Mindscapes #5, 6, 9, 23, 26 (type up #22)
Due Wednesday, 4/1
- Some statistics:
- The average American has one testicle and one ovary.
- The average income for a Lakeside School graduate was $2.5 million (in 1997)
- What's in a mean?
- Let's try a different measure of "central tendency":
The median American has no testicals and two ovaries. - What's in a measure of center?
- Visual display of data:
- What's not in a mean or median? Spread, or variation
- Activity: Heights of our class
- As a group
- Men (measure).
- Women (measure).
- Heights of people tend to be normally distributed
- Normal distributions arise quite naturally (hexstat)
- Cars
- How do we quantify variation?
- "The mean difference from the mean" is one way....
- Standard deviation is another. This is a "typical deviation" from the mean, or a "standard deviation"...
- Some other innovative, ingenious, imaginative visual displays of data
