IntMath Newsletter: Length of a curve, resources, 1000 posts

By Murray Bourne, 21 Sep 2011

21 Sep 2011

In this Newsletter:

1. Length of an Archimedean Spiral
2. 1000 blog posts. What’s next?
3. Resources
4. Poll results
5. Puzzle
6. Friday math movies
7. Final thought: Secret of getting ahead

1. Length of an Archimedean Spiral

Suitable for: Those who want to learn about polar coordinates and an application of calculus.

Watch spring - Archimedean Spiral

A reader poses a interesting question about how to find the length of an Archimedean Spiral.

Length of an Archimedian Spiral

Ananthi’s question inspired me to add 2 new sections to IntMath.com, in the Applications of Integration section:

2. 1000 blog posts. What’s next?

1000 articles

My squareCircleZ math blog has passed a key milestone – 1000 articles!

1000 blog posts. What’s next?

@IntMath on Twitter is also going well, with over 2,250 followers. Come join us – there’s a vibrant community of math students and educators sharing resources and stories.

3. Resources

Here are some useful things I’ve come across recently:

(a) Calculize

Suitable for: Everyone

Calculize is a "mathematical scripting language that runs from your browser." Their claim is you can "calculate the way you think. The core library includes advanced statistical and mathematical functions."

This is quite a sophisticated online graphics calculator.

Here are some of their examples showing how it works (click on "Run" at the top when you get there):

  • Graphics (showing a line graph and a bar graph)
  • Matrices (showing inverse, product, trace, etc)

There is a great quote on their home page:

By relieving the brain of all unnecessary work, a good notation sets it free to concentrate on more advanced problems, and, in effect, increases the mental power of the race. 
– Alfred North Whitehead, An Introduction to Mathematics

I totally agree with that one!

(b) Khan Academy

Suitable for: Everyone

I’ve written about Khan Academy before and featured some of his extensive collection of videos. There’s even a collection of videos on Singapore Math on their site.

However, Khan Academy is more than just lots of videos. Students can participate in several game-like activities where badges and awards are given out, leading to completion of a Knowledge Map.

A key difficulty most people have with math is to keep up their motivation. From all I’ve heard, these activities work well.

You can login using either a Google or Facebook account.

(c) Education World’s Using Technology in the Classroom

Suitable for: Teachers

Many teachers scratch their heads wondering how they can intelligently use technology to enhance learning. Here’s a good collection of articles outlining some useful ideas.

Using Technology in the Classroom Archive

4. Poll Results

Suitable for: Everyone

The latest poll asked readers how many of their teachers they had "friended" on Facebook. Here are the results.

None
poll 37%

One or two
poll 26%

NA – I don’t use Facebook
poll 21%

Several teachers
poll 17%

Total Votes: 1600

This is a relevant question after some US states introduced a new law earlier this year that prevented teachers communicating with their students through Facebook (or similar), with one Missouri judge blocking the law in August. It’s interesting that less than half of those who responded have a "Friend" status with their teachers, and 21% don’t even use Facebook.

Latest Poll

The latest poll asks readers about their favorite math activity. You can vote on any page in Interactive Mathematics.

5. Answer for 5 Sep puzzle

There were several correct answers to the question about the man and the lift. Of coourse, he is too short to reach the buttons for the higher floors.

(You can see the question in the 5 Sep IntMath Newsletter, and Wilson and Michael’s answers which show some further thought.)

This is an example of a puzzle where we only agonize over it once. Once we hear the answer, it stays with us forever.

New puzzle:

This week is Equinox (equal day and night, on 23rd Sep), so let’s have a calendar-based puzzle.

Julius Caesar adopted a calendar drawn up by an Alexandrian astronomer in 150 BC which assumed a year of 365.25 days. The true value is 365.242218 days. By how many days was the calendar "wrong" in 1582?

You can answer here.

6. Friday math movies

Math of music

(a) The math of sound, frequency and pitch

Suitable for: Everyone, although the level of math nudges on composite trigonometric curves and Fourier transforms.

Vi Hart gives us an enthusiastic overview of the relationship between music and math.

Friday math movie: The math of sound, frequency and pitch

A robot that flies likes a bird

(b) A robot that flies like a bird

Suitable for: Everyone

Building a robot that flies like a bird is no mean feat – but these guys have done it.

Friday math movie: A robot that flies like a bird

7. Final thought – the secret of getting ahead

Here’s a great quote from that master author and humorist, Mark Twain.

It’s a great quote because it’s very good advice. Remember it next time you’re overwhelmed with math homework (or anything you need to get done, for that matter)!

“The secret of getting ahead is getting started. The secret of getting started is breaking your complex overwhelming tasks into small manageable tasks, and then starting on the first one.” [Mark Twain]

Until next time, enjoy whatever you learn.

See the 5 Comments below.

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5 Comments on “IntMath Newsletter: Length of a curve, resources, 1000 posts”

  1. Stevens Norvell says:

    10 days

  2. James says:

    Puzzle ANS: 14 days

  3. Dilli prasad sapkota says:

    Thank you sir for sending this worthfu note .It is precious for learning mathematics.I am grateful with you for this valuable letter.

  4. Aurangzeb Khan says:

    Once you provided a website address of Math books. Can you repeat that? I shall be obliged if you do that.
    Aurangzeb Khan

  5. Murray says:

    @Aurangzeb: You can use the Search facility on any page in IntMath or the squareCircleZ blog to find past articles.

    For your convenience, here is the search result:

    free math books

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