- Homework, Section 4.7 returned (#9 and 19 graded)
- Homework, Section 4.3 is due today.
- Homework, Section 4.5 is due next time.
- For next time: Read section 7.5
- Just for fun: A honeycomb (Mother Nature, mathematician)
- 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)
- Last time we made a rubber band version of the Borromean rings, using two regular rubber bands and one cut one.
- Now we'll 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....
- 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 testicles 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 (and heads) of our class
- As a group
- Men (measure).
- Women (measure).
- Heights of people tend to be normally distributed (that is, show a bell-shaped curve):
- Normal distributions arise quite naturally
- hexstat
- Wasp masses
- 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"...
- Interpreting measures of variation (from the histogram)
