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IntMath Newsletter: Wu’s squaring trick, PatrickJMT, Google calculus

By Murray Bourne, 27 May 2014

27 May 2014

In this Newsletter:

1. Wu's squaring trick
2. Resource - PatrickJMT math videos
3. Google uses integration to speed up the Web
4. Volunteers wanted!
5. Math puzzles
6. Friday math movie: 5 Quick Math Tricks for Filmmakers
7. Final thought - walking and problem solving

1. Wu's squaring trick

Here's a neat number trick, attributed to Scott Wu, that could be a good one to impress people at your next party (depending on your social group, of course...).

You can quickly square numbers over 25 in your head. It uses this identity:

n2 = (n − 25) × 100 + (n − 50)2

For example,

622 = 37 × 100 + 122 = 3844

442 = 19 × 100 + 62 = 1936

Can you see how it works?

[Source: Wu's Squaring Trick, Quora]

2. Resource - PatrickJMT math videos

PatrickLMT

I came across Patrick JMT math videos recently. His tagline is:

PatrickJMT: making FREE and hopefully useful math videos for the world!

The extensive list of videos cover basic number and algebra, through logarithms, trigonometry and probability, to calculus.

These JMT videos are similar in style to the Khan Academy offerings, but I find them easier to follow because they're easier to watch (no black background). They are "over the shoulder"-type videos where you can see all the steps, and include plenty of examples.

The "JMT" stands for "just math tutorials".

The link again: Patrick JMT math videos

3. Google uses integration to speed up the Web

The page speed index score is based on calculus

Google tries hard to provide super-fast Web pages, and uses calculus in the process. They want everyone else to produce fast pages as well.

See how integral calculus is involved.

Google uses integration to speed up the Web

4. Volunteers, please!

I have a small task that some of you may be interested in - and you could learn something from it, too.

I made 6 short videos about integration some time ago and I need some help to transcribe the soundtrack of the videos. It just means typing out the text of my commentary.

The sound quality is not very good on those videos (they were made using Flash and then converted for YouTube) and I hope to record the soundtrack again. In the meantime, the transcription will help users to follow what is going on.

If you are studying calculus now, or will be soon, (or are just interested), this is a good opportunity to learn some of basic calculus concepts while helping me out.

If you would like to be involved, please reply to this email, or reply in the comment box.

5. Math puzzles

The puzzle in the last IntMath Newsletter asked you to find the intersection of a pulley belt with one of its wheels.

Correct answers with explanation were given by Colin, Nicos, Tomas and Don.

New math puzzle: Brigitte and Ric are sitting on their motorbikes at a rest stop beside a busy a interstate highway. They observe that the cars can be partitioned into three types, fast (120 km/h), medium (90 km/h) and slow (60 km/h). They also observe that one of each type passes every 10 seconds.

Brigitte remarks that since she always travels at 90 km per hour she can expect to overtake and be overtaken by equal numbers of cars. Ric says "nonsense", and they agree on the following bet.

Ric will pay Brigitte $1.00 for every car that overtakes her before the next rest stop if she pays him $1.00 for every car she overtakes. The next rest stop is 90 kms away.

Who wins, and by how much?

Leave your responses here.

6. Friday math movie: 5 Quick Math Tricks for Filmmakers

Film maker math tricks

This short video from Indy Mogul discusses some of the math involved in making videos.

There are many connections between the arts and math!

Friday math movie: 5 Quick Math Tricks for Filmmakers

7. Final thought - walk to solve problems

I've been doing a lot of programming lately, mostly re-writing the old Flash-based math applets on IntMath so they're mobile-device friendly.

Programming involves a lot of problem solving, where things often don't work as expected, or not at all. It can involve staring at the screen for long stretches, trying to get to the bottom of the issue.

I find one of the best problem-solving methods is to go for a walk. It's amazing how you can see things more clearly, and see the broader picture when away from the screen. Walking also increases your blood flow, and that's essential for good brain functioning.

So next time you're stuck on a math problem, go for a short walk. It will help your mental and physical health, and hopefully give you the insight you need.

Until next time, enjoy whatever you learn.

See the 9 Comments below.

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