Tuesday, April 29, 2014

Properties of 8675309

Aside from being a catchy tune, 8675309 is an integer with some interesting properties. The fact that is is a primitive Pythagorean triple is remarkable!  

wolframalpha query yields these results:



Snopes article about how this song caused (or didn't cause) havoc for phone companies...

The song:

Monday, April 21, 2014

How to make online learning succeed

Below are some general guidelines about how to make an online course work best for reasonably responsible high school students. An important philosophical belief I have based on my experience with both in-class and online learning is that "technology is a tool" and like any other tool it takes consistent practice to master and it may not be perfectly suited for every single person. It can be made to work reasonably well for almost everyone if the following guidelines are kept:

Good practices
1. There must be regular (once-per-week minimum) communication between the student, online instructor, and in-school contact.

2. The student is expected to:
2a. spend roughly 1 hour/day, 5 days/week, every week on coursework (reading the text, regularly accessing the website to see videos, notes, try problems, email instructor, etc.)
2b. ask questions as soon as a problem (tech, math, etc.) arises!

3. The student should be provided with a quiet place to work on the course. (library, quite time at computer lab, etc.)

4. Logistically speaking, tests are 90 minutes, on paper.  The student will need space, time, and a proctor for these tests. Midterm & Final = 180 minutes. Returning the tests is easy as using a smartphone or scanner to turn them into PDFs. * Note -- These times are specific to my courses. Your mileage may vary.


Here is how students often ... don't find success:

Bad practices
1. Students don't interact with the instructor regularly. Students don't have any sort of at-home or in-school person to check in on them weekly.

2. Students do the following:
2a. Spend 0 hours on the course for 2 consecutive weeks, then try to cram 10 hours into a weekend.
2b. Do not let the online instructor know when something is wrong (tech,math, etc.)

3. Students try to do their coursework in loud or distracting environments.

Myself and my team of instructors will continue to check in with the student and instructor throughout the enrollment, but the expectation is that the student is keeping to the suggestions above. Sometimes he or she may veer off course -- that's human, it happens, and it can easily be fixed if it's caught quickly.

Tuesday, April 15, 2014

Euler and more

Today's Mathematical Explorations. 

"Read Euler, Read Euler, he is the master of us all."



How to lie with dataviz: http://data.heapanalytics.com/how-to-lie-with-data-visualization/

Frequency Spectrum of sounds. (PDF)
Two letter combinations in English. http://mechanicalscribe.com/notes/most-common-two-letter-combinations/
Statistical analysis of Bob Ross's works: http://fivethirtyeight.com/features/a-statistical-analysis-of-the-work-of-bob-ross/
Depth of the ocean -- why it's difficult to find sunken black boxes. http://apps.washingtonpost.com/g/page/world/the-depth-of-the-problem/931/

Inequality in golf. And a relevant image (source)


A lexicon of common math mistakes.

Hundreds of pages of notes from Feynman.

Your weight in outer space.

census data visualization, the solar system, and engine gifs

linkdump from today's mathematical explorations

Gallery of animated gifs about engines http://imgur.com/a/eatFH
Video showing how an automatic transmission works.

Opposites do not attract, at least this is what the statistics seem so suggest.
http://fivethirtyeight.com/features/in-the-end-people-may-really-just-want-to-date-themselves/

Fantastic website for visualizing census data!
http://censusreporter.org/profiles/16000US2404000-baltimore-md/

Solar System Live: http://www.fourmilab.ch/cgi-bin/Solar

Tuesday, April 8, 2014

Fourier series and Depth of Field experiments

Linkdump from today's mathematical explorations

Interactive Fourier series visualized in d3.js http://bl.ocks.org/jinroh/7524988


Tilt Shift photography of galaxies and nebula: http://imgur.com/a/yZcOB/layout/horizontal#0

Note: "Look at the eleventh pic, for example (NGC 3621). Many of the specks of light to the left and right are other galaxies millions of lightyears away. If this were truly tilt-shift, those galaxies wouldn't be in focus." from this comment.

Also from that thread:  "What is it about tilt-shift photography that makes things seem small?"  This exists: http://tiltshiftmaker.com/ and is pretty nifty. I made the following image with it.
before (click to enlarge)

after tilt shift (click to enlarge)


Very clever sculptures which combine stone and glass.


Monday, April 7, 2014

Spectroscopy and poetry

Linkdump from today's mathematical explorations


Review of Cosmos Episode 5 "Hiding in the light" with lots of links to the scientists mentioned in the show.
http://www.latimes.com/entertainment/tv/showtracker/la-et-st-cosmos-recap-20140404,0,259862.story#axzz2yCyoagkI

Spectrosopy information:
http://loke.as.arizona.edu/~ckulesa/camp/spectroscopy_intro.html
http://www.ipac.caltech.edu/outreach/Edu/Spectra/spec.html


lunchbreak reader feed notes:
The Wikipedia article on Homer pretty drat awful...
This comment thread  illustrates why this page  is really a mess, from a historian's viewpoint. Taking everything with a grain of salt, but it seems that wikipedia has some policies that do not agree with what is commonly viewed as good academic practice. The particular article on Homer gets ~ 100k views a week, so this is a problem.

Will the social sciences ever become hard science? (very likely no, and with good reason.)
http://backreaction.blogspot.com/2014/04/will-social-sciences-ever-become-hard.html


The poetry that moves men to tears The comments of this article are full of thoughtful, insightful poems.
Anthony Holden's new anthology celebrates the poems that move men – with revealing contributions from the likes of Ian McEwan, Jonathan Franz...

From the comments section (which is just as fascinating as the article itself):
Those Winter Sundays by Robert Hayden
Those Winter Sundays
Sundays too my father got up earlyand put his clothes on in the blueblack cold,then with cracked hands that achedfrom labor in the weekday weather madebanked fires blaze. No one ever thanked him.
I`d wake and hear the cold splintering, breaking.When the rooms were warm, he`d call,and slowly I would rise and dress,fearing the chronic angers of that house,
Speaking indifferently to him,who had driven out the coldand polished my good shoes as well.What did I know, what did I knowof love`s austere and lonely offices?

Tilt and rotation of the planets.

Friday, April 4, 2014

Missing 20th century physicist, gorgeous maps

Linkdump from today's explorations

Disappearing physicist: http://www.futilitycloset.com/2014/04/02/night-crossing/ Who was Ettore Majorana? http://en.wikipedia.org/wiki/Ettore_Majorana

From an excellent stats blog: http://andrewgelman.com/2014/03/29/agree-comment/
The problem is simple, the researchers are disproving always false null hypotheses and taking this disproof as near proof that their theory is correct.
Beautiful maps made with d3.js. https://www.jasondavies.com/maps/

Thursday, April 3, 2014

Beautiful graphs and beautiful monsters

Linkdump from today's mathematical explorations

Beautifully graphs with clear explanations and interpretations are one of my favorite things.  This blog post by the 538 blog is a prime example of just that.

http://fivethirtyeight.com/features/four-strikes-and-youre-out/

While discussing counterexamples with a student today I mentioned the Weierstrass function. Here is an great blog post which gives some backstory to the development of and reaction to the function that is everywhere continuous and nowhere differentiable. A thumb on the nose to Newton.

http://nautil.us/issue/11/light/maths-beautiful-monsters
http://www.math.washington.edu/~conroy/general/weierstrass/weier.htm

The Weierstrass function is just one of many "Pathological Functions": http://en.wikipedia.org/wiki/Pathological_%28mathematics%29

There are many here http://math.stackexchange.com/questions/740/useful-examples-of-pathological-functions and here http://mathoverflow.net/questions/22189/what-is-your-favorite-strange-function.  There is also an excellent book titled Counterexamples in Analysis which covers even more of these pathological functions in great detail. http://www.amazon.com/Counterexamples-Analysis-Dover-Books-Mathematics/dp/0486428753


Cellular Automata

Linkdump from today's explorations

This reminded me of Cellular Automata and Conway's game of life.

There are 128 rules with last digit "1" 000 1 I'll have to experiment, maybe finally learn some processing, to list them all here. While searching differential equations, I found an interesting discussion about why the Navier Stokes equation is so difficult. This fits nicely into the blog post yesterday about equations. http://physics.stackexchange.com/questions/56496/what-is-the-mystery-of-turbulence/66917#66917 The solution to the equation is an open question in mathematics and you can read a very precise (2 page) description of it here: http://www.claymath.org/millenium-problems/navier%E2%80%93stokes-equation It basically describes how fluids flow.

Compressible flow (air)
Incompressible flow (water)
 

Wednesday, April 2, 2014