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Factor, Expand. Daytime Hours.

• To: mathgroup at smc.vnet.net
• Subject: [mg32299] Factor, Expand. Daytime Hours.
• From: Matthias.Bode at oppenheim.de
• Date: Sat, 12 Jan 2002 05:18:08 -0500 (EST)
• Sender: owner-wri-mathgroup at wolfram.com

Dear Colleagues,

once again I am doing maths with my son and in doing so we look for more
solutions to the textbook problems after having solved them using our
built-in biochemical processors.

So:
1.
Factor[a^2 - b^2] yields - predictably -

(a - b)*(a + b).

The question "what yields the factorization of a^2 + b^2" is not
far-fetched.

How can I coax MATHEMATICA into giving: (a - I*b)*(a + I*b)?
Are there more "simple" solutions of the same structure (... - ...)*(... +
...) or some wizardry like (... + or - ...)^t, where t is some composite
expression ?

2.
Where can I find the function that gives the daytime hours between sunrise
and sunset as a function of date and latitude?

Thank you for your help.

Best regards,

Matthias Bode
Sal. Oppenheim jr. & Cie. KGaA
Koenigsberger Strasse 29
D-60487 Frankfurt am Main
GERMANY
Tel.: +49(0)69 71 34 53 80
Mobile: +49(0)172 6 74 95 77
Fax: +49(0)69 71 34 95 380
E-mail: matthias.bode at oppenheim.de
Internet: http://www.oppenheim.de