- Your revised exams are returned.
- Your quiz 7s are returned. Here's a key
- The spiral gallery winners are in!
- Last time we talked about the story of two great physicists, Richard
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Tricks like Feynman and Bethe's are useful in real life, as
Richard found out. Here's another one: conversion to
Fahrenheit from Celsius: as already said,
But we can use an identity to make that calculation easier, as my brother discovered on our recent trip to Canada (where they, like everyone else in the world, use Celsius for temperature -- the US is alone in our love of the ridiculous "British units" -- even the Brits gave up on them!):
I hope that you'll agree that
.
The reason why this formula is easier is because of the operations required to compute. Think of it this way: given C, double it, subtract 10 percent of that, and add 32:
So
- What's C=100 in Fahrenheit?
- What's C=0 in Fahrenheit?
- What's C=50 in Fahrenheit?
- What's C=-40 in Fahrenheit?
- Strogatz gives another example of a useful algebraic formula:
presenting it in the context of the stock market; and he ends with the "icky relationship" formula:
Your partner in a relationship, where your age is x, should be at least
: so your partner's age y should satisfy
in age. What do you think? Let's look at some example, and compute the range of relationship ages you can consider to be "non-icky".
You must not be too young for your partner, either: hence
which we can solve for y, to yield
Putting them together, we get the "appropriate partner age relationship:"
I'm x=52, so my range is
Fortunately my wife falls somewhere in that range....
- So where did algebra come from? 9th century Arabic mathematician al-Khwarizmi ("algorithm") is credited: consider the problem
al-Khwarizmi solved this by "al-jabr" -- restoration (or what we call "completing the square" -- restoring the square). We'll take a look at his solution, on p. 71, and then a few variants of that today.