# MathArguments180.com

180 Days of Ideas for Discussion in Math Class. (as of 9July2014, we're in overtime!)

## Sunday, October 11, 2015

### 495: Pythagorean anti-Triples?

Ask your class if there are any Pythagorean anti-Triples: $\dfrac{1}{a^2} + \dfrac{1}{b^2} = \dfrac{1}{c^2}$ ?

If a, b, c are integers, the question seems harder, since 1/3, 1/4, 1/5 would be (to me) obvious answers - leading to the rules for Pythagorean triples and just using their reciprocals.

Source:

```
Are there any Pythagorean anti-triples: 1/(a^2) + 1/(b^2) = 1/(c^2) ?
— James Tanton (@jamestanton) October 11, 2015
```

## Saturday, October 10, 2015

### 494: NetFlix Optimization

An article about the Netflix price hike:

Netflix upped the rate of its “two-screen” plan from $8.99 to $9.99. This plan lets you watch two HD (or regular) streams simultaneously on different devices. Netflix’s “one-screen” and “four-screen” plans remained unaffected.

Here's the thinking: If Netflix subscribers start dropping from the two-screen plans to one-screen plans, this will make them a lot less likely to share their password. No one wants a little offhand altruism to actually affect their viewing habits. That would be bad. If the resulting lack of password-sharers pushes more people to subscribe, then its worth the dollar per subscriber Netflix loses when a user downgrades because of the price increase.

Find the NetFlix subscription numbers to see how the price hike changed things. Was this a good move?

## Tuesday, September 29, 2015

### 493: It Sure Would Be Easier

If we are told that we have a quadrilateral inscribed in a circle with diameter 10, do we

*if the angle at B and the angle at D are 90°? Because that sure would make it easier to find x.***KNOW**## Sunday, September 27, 2015

## Sunday, September 13, 2015

### 491: Discuss the Errors, part 2

This question is from the NY Regents test, and discussed by Patrick Honner in his long-running series, "Are These Tests Any Good?".

Can your students find what is wrong with it?

How would they fix it?

source.

Can your students find what is wrong with it?

How would they fix it?

source.

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