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Conference rusure::math

Title:	Mathematics at DEC

Moderator:	RUSURE::EDP

Created:	Mon Feb 03 1986
Last Modified:	Fri Jun 06 1997
Last Successful Update:	Fri Jun 06 1997
Number of topics:	2083
Total number of notes:	14613

2060.0. "more whimsicalia (arcsin(2))" by PAWN21::OSMAN (see HANNAH::IGLOO$:[OSMAN]ERIC.VT240) Fri Aug 30 1996 16:17

The froops note (2059) brought up the idea of whimsical math.

Originally, we "couldn't" take the square root of negative numbers, so
someone whimsically(?) named the nonexistent value like this:

	i = sqrt(-1)

and built all of complex numbers on this nonexistent value.

o.k. Here's another nonexistent thing.  All angles have a sine not exceeding
1.  So how about we name

	a = arcsin(2)

That is, a is the nonexistent angle whose sine is 2.

Can we build anything interesting on this ?

/Eric

T.R	Title	User	Personal Name	Date	Lines
2060.1	complex numbers?	FLOYD::YODER	MFY	`Fri Aug 30 1996 16:29`	14
	I think that "all" you get are complex numbers. That is, if x = arcsinh(2) then ix = arcsin(2) is "merely" an imaginary number. So your second example is arguably the same as the first! ix -ix In C, sin(x) = (e - e )/2i.
2060.2		RUSURE::EDP	Always mount a scratch monkey.	`Tue Sep 03 1996 08:42`	11
	In Derive (or most symbolic math packages), enter asin(2) and simplify to get: pi/2 - i ln(sqrt(3)+2). -- edp Public key fingerprint: 8e ad 63 61 ba 0c 26 86 32 0a 7d 28 db e7 6f 75 To find PGP, read note 2688.4 in Humane::IBMPC_Shareware.
2060.3	if sin(a) = 2 then ...	PAWN21::OSMAN	see HANNAH::IGLOO$:[OSMAN]ERIC.VT240	`Tue Sep 03 1996 09:51`	16
	sin(a) = 2 sin^2 + cos^2 = 1 so 2^2+cos^2 = 1 cos^2 = -3 cos(a) = sqrt(-3) Does this help ? /Eric
2060.4	re: .3	BEGIN::YODER	MFY	`Tue Sep 03 1996 10:18`	9
	>Does this help? It helps in that it suggests that the arcsin(2) extension might be related to the sqrt(-1) extension (and we know that it is). You have hit upon a problem that happens to be solved, though I wouldn't mind if this turned into a discussion of functions over the complex plane (especially if it became a discussion of algorithms).