OkTrends - The Math of Dating

OkTrends is a blog run by the folks at the matchmaking website OkCupid. Their website generates huge volumes of data on personalities, attraction, and sex and they've been crunching those numbers to see what interesting relationships pop out.

For example, in this graph Christian Rudder graphs how attractive people appear in their photos based on the time of day the photo was taken:

From OkTrends - Don't Be Ugly By Accident

In the graph, the blue line is the average attractiveness of photos grouped by time of day. Superimposed on that trend is another graph in yellow and brown of the height of the sun during the day and night. When the sun crosses the horizon that's sunrise and sunset. Mr Rudder is able to show evidence of Golden Hour; the hour after sunrise and before sunset when vivid colors fill the sky and make pictures more interesting.

There's tons of SL Math in this blog. Mr Rudder fits a sinusoidal curve to the attractiveness data in an attempt to show that photos taken in the afternoon and late at night are often most appealing.

From OkTrends - Don't Be Ugly By Accident

I'm planning to add this graph to my unit on sine and cosine. I imagine the discussion will be memorable

• What does the trend suggest about good photos? 
• Does the trend appear to be a good fit of the data?
• What is the period of the graph? Would it have been reasonable to expect the period to be 24 hours?
• If you were to perform the same study from scratch, how would you do it?

Finally, here's a graph comparing the number of (self-reported) sexual partners straight men and women have had to gay men and women:

From OkTrends: Gay Sex vs. Straight Sex

After thinking, "Wow, those trends are very similar," my next thought was, "Is that an Ogive?!" It seems like the only place I ever see Cumulative Frequency Charts is in IB exams but here's one in the wild!

Some questions I might ask students are:

• Where do the two trends differ the most? What does that mean about the similarities and differences between the sexual habits of the gay and straight communities?
• How many partners has the median straight/gay person had?
• If this graph were to be turned into a frequency distribution, what shape would it have?
• Followed up with: All of this data is self-reported. If respondents were to lie, what kinds of lies might they tell and how would that effect the shape of the expected distribution?

Some of the topics in the blog are a bit too racy for my classroom, but there are still a lot of useful gems. Honestly the whole thing is just fascinating.

Math Extension - Ancient Greek Geometry

Here's a fun puzzle I found out about recently. It's called Ancient Greek Geometry. The challenge is to create different shapes (like triangles, and circle patterns) using only a straight-edge and a compass. For example, here's a solution for a hexagon:

Hexagon Created Using a Straightedge and Compass

The program runs right in your browser and is easy to learn. Just point your students to the website (http://sciencevsmagic.net/geo/) and they'll figure out the rest.

There's also a number of other neat features from the same people at their website.

http://sciencevsmagic.net

f.lux - Use your montor's Color Temperature to help manage Sleep Schedules

We all know the importance of Sleep Schedules and getting enough sleep, especially to students. If not, check out this article discussing recent research on Sleep Deprivation and Academic Performance in Students. (SPOILER: Sleep deprivation inhibits learning).

Modern students face a double-whammy:

1)      We ask a lot from them

2)      They do their work on their computers

Together, these factors often lead our students to face their laptop screens up until they go to bed. According to this article discussing the relationships between screen brightness and sleep schedules, staring at a bright screen at night tricks your brain into thinking it’s daytime, preventing your brain from getting properly ready for bed and ruining your sleep schedule.

Enter f.lux, a program which will automatically adjust your screen’s color temperature during the day to mimic a sunset.

I've been using this program at home for years now and I love it. Before, I used to have to stop using my computer an hour before bed or I wouldn't feel tired. Now, I could fall asleep sitting up while reading at my computer. Best part: It’s free, so no harm in trying it. It takes about a day to get used to it and then you’ll wonder how you got by without it.

New Videos in Math SL and Physics HL Extension

I've been on vacation this week so I got off my butt and made a pair of videos on two topics that I find interesting.

First we have acceleration of a rocket with changing mass. In Physics HL we only ever deal with changing accelerations by looking at graphs but I wanted to go through the calculus to find the exact (well kinda) answer. In the end, probably due to some of the assumptions I made, I was off by a factor of 2.

In this video, I attempt to find the top speed of the Saturn V rocket if it were already free from earth's gravity and fully fueled.

Second we create an interesting shape by cutting into the side of a cylinder. Almost 10 years ago when I was still a university student on an internship, one of the drafters asked me what the volume of a circular cut out of the side of a cylinder would be. He already knew the answer, but I guess he wanted confirmation. I wasn't so great at calculus at the time and I didn't have any 3D software to help me visualize the shape so it took me three days to arrive at the answer. In the end I was surprised at how easy it was when you looked at the shape the right way.

Unit Circle Snypa

I find that my students always seem to have difficulty with the unit circle. In class, we work on understanding the symmetry in the circle, and what the meaning of the values are. However at the end of the day they need to be able to reproduce the major angles and that skill comes from practice.

To help them, I made a unit circle flash card program, Unit Circle Snypa.

Download Unit Circle Snypa for Free

The upper button cycles to the next question, the lower button suggests hits (right-hand side)

It randomly quizzes the user on sine, cosine, tangent, and the inverse trigonometric functions. You can also just quiz angles in radians or degrees.

You can quiz any combination of these functions.
Alternatively,  de-select all the functions and just work on angles alone

Unit Circle Snypa can also offer progressive levels of hints to the students if they get stuck.

Hints are offered progressively. Students can get a hand, without getting the whole answer.

I gave the program to my students for practice at home, but I'll also run the program in class if we finish the lesson five minutes early. I find that it works well side-by-side with my random student selector, Popsicle Shticks. My students have been getting better but we'll still need more practice.

You can download Unit Circle Snypa for free, here. The source code is also available, here. I hope you find it helpful!

Two-Envelope Paradox

The Two-Envelope Paradox is an interesting puzzle about probability. You can read more about it at wikipedia, or join the discussion.

In short, there are two envelopes, A and B, and one contains twice as much money as the other. You're holding envelope A in your hands. Before looking in either envelopes A or B, does it make sense to switch to envelope B?

On the face of it, it seems that it doesn't matter whether you switch or not. However a "paradox" arises if you choose to think of the contents of envelope B as containing half or double that of A. Meaning you have even odds of doubling or halving your money. Under this assumption, it makes sense to switch, as you stand to gain more than you risk losing!

My explanation of the "paradox" is below if you're interested:

Popsicle Shticks 1.02 - Bug Fix

One of my students recently notices that she always seemed to be the last person on the group list. Since the class has 22 students in it, that meant that she ways always the odd woman out when we had groups of 3. A quick investigation showed that this was a bug!

I tracked down the source to a poor assumption about how Random.Next(lower, upper) worked. It turns out that it does not include the upper-bound as I had thought, meaning the group generator wasn't considering the last person on the class list until they were they were the last person to be randomly sorted into a group.

Anyway, you can download the updated version of Popsicle Shticks here. Source code here. Original Post here.