IntMath Newsletter: trig differentiation applet, art, music
By Murray Bourne, 24 Jan 2017
24 Jan 2017
In this Newsletter:
1. Differentiation applet - trigonometric functions
2. Math art
3. Resource: SimplexNumerica
4. Math movie: Music And Measure Theory
5. Math puzzles
6. Final thought: Challenges
Happy New Year and Gong Xi Fa Cai!
Today's Newsletter has a cultural (art & music) focus.
1. Differentiation interactive applet - trigonometric functions
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In this applet you can explore the shapes of the six trigonometric functions (sin, cos, tan, csc, sec and cot) and their derivatives. See: Differentiation Interactive Applet - trigonometric functions |
You can see some background on this interactive in these three earlier articles:
Explore the slope of the sin curve
Explore the slope of the cos curve
Explore the slope of the tan curve
2. Math art
I spotted this great piece of 3D art based on mathematical principles at a recent exhibition at the Art Science Museum in Singapore recently. It's like warped sine curves projecting out from a surface.
For me, it's a soothing image which promotes reflection.
3. Resource: SimplexNumerica
Here's a useful zero-cost offering: SimplexNumerica
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SimplexNumerica produces high quality 3D math graphics, including surface plots, data analysis and visualization; and 2D contour, Gantt, finance and vector charts. See: |
Here are some sample screen shots, showing a contour plot and a polar vector plot.
SimplexNumerica is available in 32-bit and 64-bit Windows versions (but no Mac or Linux versions, unfortunately).
4. Math movie: Music And Measure Theory
There's a very clever series of videos that relate math concepts in animations over at 3blue1brown. I'm going to feature some of them here and in future Newsletters.
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Music and Measure Theory ties in Pythagorean ratios in music (why do some chords sound better than others?) with covering a dense set in the reals with open intervals whose lengths sum to an arbitrarily small constant. |
It sounds scary, but it's very well illustrated and for the most part, easy to follow. See:
5. Math puzzles
The puzzle in the last IntMath Newsletter asked about writing the digits of 2017. There were no submissions, but I'll leave it open. This task could be a good class exercise for practicing mental number operations.
New math puzzle: Geometric progression
Find the least number of terms of the following geometric progression such that 2 − N < 0.0001.
You can leave your responses here.
6. Final thought: challenges
Image source
It often seems that happiness comes from enjoyable but challenging pleasures, and involves few possessions. This is what Einstein had to say about it:
A table, a chair, a bowl of fruit and a violin; what else does a man need to be happy? [Albert Einstein]
Until next time, enjoy whatever you learn.
See the 9 Comments below.
