### 35 years ago

35 years ago today I set out on a strange journey, to a city with a name great among the cities of history. It I had not gone there, it is quite unlikely I would be here today, doing what I do. It was there that I learned about computers - from a computer great among the computers of history.

While I was there, I got to play with a two-million dollar spirograph. It was a lot of fun. (Yes, I wrote the code to do that... and they say trig isn't important? Ha!)

"Down in Packard 118Posted in memory (60 bits!) of the CDC 6400, and also in fond recollection of many good friends and difficult foes... some who are now departed from the earth:

Sits that evil bit machine,

Guarded by its faithful servants night and day..."

*Requiem aeternum dona eis Domine: et lux perpetua luceat eis.*

Requiescant in pace. Amen.

Requiescant in pace. Amen.

Some day - maybe April 5 - I will tell you about the other city (which also has a name great among the cities of history!) where I got my third degree, and so became the one you now know as

*Doctor*Thursday.

P.S. I forgot to put this in. I was thinking about the complexities of going back to college... Ahem. There is a great movie called "The Brave Little Toaster" which is based on a great book by the same name. There's a hilarious scene where "The Master" that owns the Toaster ("The Master"'s real name is Robbie) is getting ready to go to college, and his mom asks "Do you have enough socks?" The scene shows rows and rows of folded socks stacked on his bed, and Robbie says "I got enough to stock the dorm! I'm not going to Jupiter, Mom! It's only college."

Sigh! Sometimes I wish I

*had*gone to Jupiter - there's lots less gravity there. but that's why I'm in business... We need more laughter - we need (as Chesterton says) to learn to take ourselves lightly! That's why I took that class in Advanced Spirograph. I got an "A" but it's not on the transcript. Hee hee.

For your homework, write a composition on what

*you*did 35 years ago today, and then derive the equations for the sine and cosine of the sum and difference of angles:

Given two angles a, b, their sines and cosines, find:

sin(a+b)

cos(a+b)

sin(a-b)

cos(a-b)

Show all work. No cheating.

(I can still do this. That's why I got the "A".)

## 2 Comments:

Thirty-five years ago ... my parents were in grade school. ;) (They were both ten.) But I, alas, was doing nothing. What are the sine, cosine, and tangent of zero?

Oh... sorry... I forget I am old now.

Here are your answers:

sin(0) = 0

cos(0) = 1

tan(0) = 0

Alas. I wonder if even computer people learn trig these days?

The first rule of trig on computers: avoid it if you possibly can. That's why these alternative forms of equations are such delights. We might call it a kind of "periphrastic" math... Like the exceedingly powerful "Calculatus Eliminatus" of the "Cat inthe Hat": we compute sines and cosines by

notcomputing them, but by computing something else that's equal to them.(Actually trig functions on computers cheat. But I'm not supposed to tell you that.)

Hee hee.

--Dr. Thursday

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