(Mathhombre) Miscellanea

Manhole.

Patrick Honner is a math teacher in New York who also takes some amazing math-inspired photos of the city. His manhole picture inspired this sketch.

On GeoGebraTube.

Intersections, Anila Quayyam Agha, Art Prize 2014

Heather Harrington and I are doing a #mathart activity at Super Science Saturday based on this piece from art prize. All of her work is pretty delightful - see more at anilaagha.squarespace.com

A passage from Avot (The Fathers) in the Mishnah. Avot 5:15 says: ‘there are four types among them that sit in the presence of sages’.

In other words, according to the rabbis there are four types of disciples – the sponge, the funnel, the strainer, and the sifter (sieve).

1.   The sponge – it soaks up everything. … a disciple who has no discernment—he just takes it all in and records it all; the trivial and the important; it doesn’t matter — there is no discrimination on his part.

2.   The funnel – it takes in at this end and lets out at the other. … We could say that is the student who is quick to perceive, but he is equally quick to forget. He is very bright, he takes in very quickly, but then he forgets it equally quickly.

3.   The strainer – it lets out the wine and collect the lees. This person is the one who forgets the essentials but retains the unessentials. … they can recite the most obscure trivia from the Bible, but when it comes to the important stuff, they don’t know it.

4.   The sifter – it extracts the coarsely ground flour and collects the fine flour. This is the kind of disciple that the rabbis most admired – the one who memorizes the good in all the material but rejects the worthless; he retains what is good and excellent and he rejects what in unimportant and what is trivial. The rabbis were always interested in a student’s discernment, a student’s skill at learning; not just mere repetition. It didn’t impress a rabbi if you have photographic memory. 

Paraphrased and abridged slightly from Dwight Prior from a Hebrew/Christian religious series. Those rabbis clearly knew their students!

Polygon Pattern.

Any questions?

(Note: finally carried out a successful Execute command for this, to make separately coloring rows a little easier. EDIT: added a zoomed out gif.)

Among all the counting questions, I like this one for the “does the first step fit the pattern?”

Mountain or fountain?
One without the randomness.

Mountain or fountain?

One without the randomness.

Chained Parabolic Arcs in a Circular Sector.

Not sure what got these images in my head. Too long to make, and it took Michael Borcherds’ help to finish. It turns out there are situations that the Function[<fn>,<lower bound>,<upper bound>] - my usual go to for limiting domain - doesn’t work. Like in a sequence command. @mike_geogebra said I could use If[ ] instead. Like If[0<x<10, x^2]. Thanks!

This also pointed out I still don’t understand the Execute command, and can’t find a good primer. Know one?

If you want the GGB file for some reason, just let me know.

Better Coupon.
Saw these coupons and thought it was a nice little rational number situation. Tweeted the coupon, then made a GeoGebra visualization.

Better Coupon.

Saw these coupons and thought it was a nice little rational number situation. Tweeted the coupon, then made a GeoGebra visualization.

sigfodr:

A version for tumblr that can be read without opening a new tab, since plenty of people would scroll past this story otherwise.

source: Zen Pencils

Education should be a right, but is instead a privilege.

Octagon Packing.

The AMS have a post explaining a pretty sweet result about the best octagon packing. But it’s not dynamic! Enter GeoGebra… I added the slider so you could make the approximation more accurate.

On the tube: http://www.geogebratube.org/material/show/id/192477

Staircase Pattern.
For Matt Coaty&#8217;s students. (It was fun to make.) Corresponds with Fawn Nguyen&#8217;s visualpatterns.org Pattern 39
If anyone want&#8217;s the GeoGebra, I&#8217;d be happy to upload it.

Staircase Pattern.

For Matt Coaty’s students. (It was fun to make.) Corresponds with Fawn Nguyen’s visualpatterns.org Pattern 39

If anyone want’s the GeoGebra, I’d be happy to upload it.