I enjoy making students draw diagrams like these in their notes. You’ll never understand how difficult it is to draw mutually tangent circles until you try to do it yourself!
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We always end up arguing about stuff like this in my class.
For more images from math class, check out my Facebook page.
As usual, I wasn’t thrilled when my landlord told me about this year’s rent increase. As someone familiar with how exponential growth works, I understand the power of the small, consistent percent increase.
After some mild protests, the landlord came back with some good news: he was going to reduce my increase by $25 per month! I wasn’t exactly thrilled with that, either, but it’s a gesture. And I thought to myself “At least I won’t be paying future increases on that $25!”
Which got me thinking: if my rent goes up 3% every year, how much of a difference will that $25 make? The answer: not much. In my lifetime, anyway.
At 3% per year, the $25 difference in rent now will be a $30 difference in 5 years. In 15 years, the difference in the two rents will be around $40. And if I stick around for 50 years, the difference will be about $90.
If I could stay here for 200 years, I’d see a big difference: almost $10,000! But then again, my rent would be around $1 million per month.
I’ll have to be content knowing that, while in the short term I don’t see much benefit, I win out as t goes to infinity.
After having fun exploring rigid and non-rigid frames, I hung one of our indeterminate quadrilaterals up on the board. The next day, we were proving a theorem about orthodiagonal quadrilaterals, and the final step concluded that a particular quadrilateral was actually a rectangle.
I found a cute little spot to finish our proof.
This elicited a few laughs from students who appreciated the irony.
But apparently, some students in a later class did not appreciate it. They felt the need to chime in.
As a general rule I must oppose mathematical graffiti, but it’s hard not to respect their position.
This is an excellent, in-depth video on the mathematics of juggling, from Cornell University professor (and world-class juggler) Allen Knutson.
http://www.youtube.com/watch?v=38rf9FLhl-8
This hour-long video covers the mathematical notation developed to classify and communicate juggling patterns, and Knutson explains how that inherent mathematical structure can be used to create new patterns.
There’s a lot of very sophisticated math here, which may surprise some people. But as Knutson says at the beginning, “Anything that is sufficiently understood … there should be a mathematics of that thing.”
There’s also some good juggling in here, too!