## Taylor series

Today, XKCD, with tongue in cheek, is saying that “The Taylor series should have been canceled after the first term”.

After a flying visit to London (more about that shortly), I am reminded again that at least the second term of the Taylor series impinges on real life.

My house in London is in a courtyard entered through double gates hinged at the outside. By entering a code, you can open either a single or a double gate. The gates are rather slow to open, and of course I get impatient.

Assume for simplicity that the width of each gate is one unit of length, and that the gates open at 1 radian per unit of time. Now, if I open a single gate, then after time t, the gap for me to get through is 2 sin t/2, whose Taylor series is t+…; while if I open both gates, the gap is 2(1−cos t), whose Taylor series is t2+…

I have watched people waiting for the double gates to open wide enough for them to slip through, and grumbling about the slowness. Of course I feel a little smug!

## About Peter Cameron

I count all the things that need to be counted.
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### 4 Responses to Taylor series

1. QM says:

What you don’t say, is how wide the gap must be for you to pass, and whether that happens in each case at t1.

2. QM says:

t < 1, or t > 1

• These are slow-moving gates. It would probably take around 20 seconds for them to open one radian. As to the first question, the double gates are wide enough for a car or van to get through (that is twice my unit of length), and I am not very wide. So t is quite small.

3. Jon Awbrey says:

Taylor Series for Boolean Functions

Just a little sum thing to play a round with …

Jon

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