On Sat, Jul 18, 2015 at 4:01 AM, David Jeffrey <djeffrey@uwo.ca> wrote:

Derive (God bless its bits and bytes) can simplify all of these expressions automatically. It does it by reducing each acos to a canonical atan. Then the two atans cancel.

Derive, you may remember, was bought by TI and then withdrawn from the market.

David Jeffrey U. Western Ontario

You bet I remember. Albert Rich sold it to them but they paid him to continue enhancing it. He hired me to help. We made exhilarating progress for eight weeks. Then TI pulled the plug. They seem to be a completely uncreative, green-eyeshade company, but I'm not sure they bought Derive with the intention of destroying it. Danny Hillis has some amusing stories of their corporate espionage endeavors. There was also some craziness about them de-implementing the Gamma function on their calculators because it gave students in certain countries an unfair advantage. They also knocked off the Symbolics Lisp Machine(s) (TI-Explorer). But it's unclear they had much to do with the death of Symbolics, as much as they might have welcomed it. --rwg

On 2015-07-16 18:56, rwg wrote:

...

On 2015-07-16 08:27, Warren D Smith wrote:

...

It is interesting that some of the most-amazing among the listed miracles involve only powers of 2 in denominators:

5*acos(-7/8)+2*acos(-61/64) =1080.0 4*acos(-57/64)+5*acos(-31/32) =1440.0 1*acos(57/64)+5*acos(-3/4) = 720.0 1*acos(61/64)+5*acos(-1/4) = 540.0 4*acos(-3/4)+1*acos(-31/32) = 720.0 2*acos(-3/8)+1*acos(-23/32) = 360.0 2*acos(5/8)+1*acos(7/32) = 180.0 3*acos(-17/32)+4*acos(-11/16) = 900.0 ...

Hey, 3-4-5 ! In[905]:= 3*ArcCos@(-17/32) + 4*ArcCos@(-11/16) == 5*Pi

In[906]:= FullSimplify[%]

Out[906]= 3 \[Pi] == 6 ArcSin[17/32] + 8 ArcSin[11/16]

is dumfounded, too. --rwg

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