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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

Taylor Maclaurin Series interactive applet

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.

math art

For me, it's a soothing image which promotes reflection.

3. Resource: SimplexNumerica

Here's a useful zero-cost offering: SimplexNumerica

SimplexNumerica screen shot

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.

surface plot
polar vectors
[Images: source]

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.

Music And Measure Theory

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:

Music And Measure Theory

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

Einstein with his violin
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.

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