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### The Math of Time

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Date: 05/15/97 at 11:30:13
From: andrew wainio
Subject: The math of time

I'm a college art student who knows nothing of math.  I'm currently
trying to figure out whether there is a connection between math and
time, possibly behind the science of how a clock works. Do you have
any information that would help me?

Thank you.
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Date: 05/23/97 at 14:45:13
From: Doctor Bill
Subject: Re: The math of time

Dear Andrew,

There is a connection between math and time. In fact, all time has to
do with math. Think of the earth as a big clock. It turns 360 degrees
in 24 hours, so it turns 15 degrees each hour. This is how we figure
time zones, each of which is 15 degrees wide.

Also, the sun appears to move north and south throughout the year
because of the tilt of the earth on its axis, the earth's rotation on
its axis, and the earth's revolution around the sun. If the earth
didn't rotate, then part of the earth would be in complete darkness
all of the year and the other part of the earth would always be in
daylight.  (Because the moon makes one rotation on its axis in the
same length of time it takes for for it to make one revolution around
the earth, we only see one face of it - hence "the dark side of the
moon.")

Here are a couple of experiments you can do. You can construct a
sundial by putting a stick in the ground that angles toward north at
an angle equal to your latitude. If your latitude is 40 degrees north,
have the stick at an angle of 40 degrees with the ground. Then the
shadow it casts will tell you the time, with due north being 12
o'clock noon (remember to adjust for daylight savings time).

Since you are an art student, you might be more interested in an
analemma. Put a vertical stick in the ground and then each day for a
year, mark where the tip of the shadow is at the same time each day.
It doesn't matter what time of day you make the marking - just as
long as it's the exact same time every day. You also don't have to do
it every day since the sun doesn't change its position in the sky by
that much over the course of the day. Just make sure that you do it
at least one day a week. Of course, the more marks you make, the more
accurate your analemma will be. The marks you make will trace out a
figure called an analemma. It is a figure eight, and it will show you
the movement of the sun throughout the year.  Astronomers call this
the "equation of time" because you can use it to adjust the time that

-Doctor Bill,  The Math Forum
Check out our web site!  http://mathforum.org/dr.math/
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