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IntMath Newsletter: Fourier interactive, 2012 summary

By Murray Bourne, 18 Dec 2012

18 Dec 2012

In this Newsletter:

1. New interactive: Fourier Series
2. Christmas
3. Most popular articles of 2012
4. Looking ahead - 2013
5. Math puzzles
6. Friday math movie: The Mathematics of History
7. Final thought - treating others

This is the last IntMath Newsletter for 2012. It's a bumper issue with lots of (hopefully) interesting reading.

1. New interactive: Fourier Series

Fourier Series graph interactive

Here's an interactive graph that allows you to explore the concepts behind the Fourier Series.

Fourier Series interactive graph

2. Christmas

(a) An engineer's view of Santa Claus

Santa's Christmas Eve physics

Here's a fun mathematical analysis of Santa's frantic dash around the world every Christmas Eve.

An engineer's view of Santa Claus

(b) 12 Days of Christmas

Each year at this time, my article The Twelve Days of Christmas – How Many Presents? has many readers.

3. Most popular articles of 2012

One of the joys of writing a newsletter is getting a lot of appreciative feedback. Another is to see which articles you enjoyed the most, and to use this information to plan future Newsletters.

Here are the most popular IntMath Newsletter items during 2012 (based on traffic).

Resources & math articles

  1. Free Textbooks in Mathematics (no longer available)
  2. Modelling Fish Stocks
  3. Absolute value of a complex number
  4. Today is e-day
  5. Wolfram Education Portal
  6. Desmos Graphing Calculator


  1. Interactive Ellipse Graphs
  2. Radius of Curvature interactive graph
  3. Conic Sections 3-D interactive
  4. Differentiation interactive graphs
  5. Biorhythm graphs


  1. Video: How it feels to have a stroke
  2. Hans Rosling on Religions and Babies

4. Looking ahead - 2013

Here are a few things coming up for 2013.

(a) 2013 is year of Math of Planet Earth

The aim of Mathematics of Planet Earth 2013 is to examine the role mathematical sciences play in the challenges facing our planet and our civilization. As they say:

More than 100 scientific societies, universities, research institutes, and organizations all over the world have banded together to dedicate 2013 as a special year for the Mathematics of Planet Earth.

The site has articles about using mathematical models to eradicate disease, the Equation of Time and How does GPS work?

(b) Free online Calculus course starts 7th Jan

Another MOOC (massively online open course) starts 7th January 2013. This time it is an Introduction to Calculus.

The instructor is Robert Ghrist from the University of Pennsylvania. I like where they say the course will have "an emphasis on the conceptual over the computational".

These MOOCs are quite an experience. The last one I joined was Keith Devlin's course on Mathematical Thinking. There were over 60,000 of us involved in that course.

See Calculus: Single Variable for more information and to sign up.

5. Math puzzles

Answer for last puzzle: The puzzle in the last IntMath Newsletter concerned adding fractions. The correct answer was 2475. Those who were correct and showed correct working were: Miguel, John Cherpak, Colin Fraser, Devanie, Thomas A. Buckley, Yeoh Kiat Boon, Guido, Nicos, Tomas, Vasu, Arun, Tom Barrett, Rosa, Ronak (who also included a C program routine), Dineth, and Lachezar.

New puzzle: If n is an even positive integer, how many positive integer solutions are there for 2x + y + z = n? (Express your answer in terms of n).

Leave your responses here.

6. Friday math movie: The mathematics of history

Math of history

What's the connection between verbs, math and hip hop?

Friday math movie: The mathematics of history

7. Final thought - Treating others

It's that time when many of us reflect on the past year, and make plans (and resolutions) for the coming one.

The final thought for 2012 is quite global, but can also relate to math learning and the instructor-learner relationship. It's also a good thing to keep in mind for all the interactions we have with those around us.

Each major religion has some suggestions on how we should treat others, known generally as the Golden Rule.

Buddhism: "Hurt not others with that which pains yourself."

Judaism & Christianity: "You shall love your neighbor as yourself."

Islam: "As you would have people do to you, do to them; and what you dislike to be done to you, don't do to them."

Hinduism: "One should always treat others as they themselves wish to be treated."

Sikhism: Recognize all of mankind as a single caste of humanity and accept all humans as your equals.

Zoroastrianism: "Whatever is disagreeable to yourself, do not do unto others."

Confucianism: "What you do not want done to yourself, do not do to others."

In summary, "Treat people the way you'd like to be treated".

The IntMath Newsletter will return in mid-Januray. Enjoy your Christmas and/or New Year holiday season.

Until next time, enjoy whatever you learn.

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