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!