New guy and programming problem
09-02-2018, 07:33 PM
Post: #35
 Thomas Klemm Senior Member Posts: 2,078 Joined: Dec 2013
RE: New guy and programming problem
Fun fact: These trigonometric identities were used for multiplication and division before logarithms were known.

Cf. Prosthaphaeresis
Quote:Notice how similar the above algorithm is to the process for multiplying using logarithms, which follows these steps: scale down, take logarithms, add, take inverse logarithm, scale up. It's no surprise that the originators of logarithms had used prosthaphaeresis. Indeed the two are closely related mathematically. In modern terms, prosthaphaeresis can be viewed as relying on the logarithm of complex numbers, in particular on Euler's formula:

$$e^{ix}=\cos x+i\sin x$$

I find it interesting that this technique was developed using complex numbers under the hood while they weren't discovered yet.

Cheers
Thomas
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 Messages In This Thread New guy and programming problem - Skirmitch - 08-27-2017, 06:18 AM RE: New guy and programming problem - Dieter - 08-27-2017, 03:15 PM RE: New guy and programming problem - Gerson W. Barbosa - 08-27-2017, 05:12 PM RE: New guy and programming problem - Dieter - 08-27-2017, 05:43 PM RE: New guy and programming problem - Paul Dale - 08-27-2017, 11:12 PM RE: New guy and programming problem - Dieter - 08-28-2017, 06:13 PM RE: New guy and programming problem - Paul Dale - 08-29-2017, 04:22 AM RE: New guy and programming problem - Garth Wilson - 08-27-2017, 09:14 PM RE: New guy and programming problem - Vtile - 09-01-2018, 07:28 PM RE: New guy and programming problem - John Keith - 08-27-2017, 05:52 PM RE: New guy and programming problem - Dieter - 08-27-2017, 06:28 PM RE: New guy and programming problem - Gerson W. Barbosa - 08-27-2017, 06:03 PM RE: New guy and programming problem - Dieter - 08-27-2017, 06:11 PM RE: New guy and programming problem - Gerson W. Barbosa - 08-27-2017, 06:23 PM RE: New guy and programming problem - pier4r - 08-27-2017, 07:52 PM RE: New guy and programming problem - Jlouis - 08-28-2017, 10:55 AM RE: New guy and programming problem - Skirmitch - 08-27-2017, 06:04 PM RE: New guy and programming problem - Skirmitch - 08-28-2017, 01:44 AM RE: New guy and programming problem - Paul Dale - 08-28-2017, 01:58 AM RE: New guy and programming problem - Skirmitch - 08-28-2017, 02:25 AM RE: New guy and programming problem - Paul Dale - 08-28-2017, 05:31 AM RE: New guy and programming problem - Skirmitch - 08-28-2017, 07:14 AM RE: New guy and programming problem - ndzied1 - 08-28-2017, 03:43 AM RE: New guy and programming problem - Paul Dale - 08-28-2017, 07:28 AM RE: New guy and programming problem - Logan - 08-28-2017, 02:20 PM RE: New guy and programming problem - Skirmitch - 08-28-2017, 06:11 PM RE: New guy and programming problem - Logan - 08-28-2017, 06:13 PM RE: New guy and programming problem - Thomas Klemm - 09-01-2018, 12:23 PM RE: New guy and programming problem - Albert Chan - 09-01-2018, 02:16 PM RE: New guy and programming problem - Albert Chan - 09-02-2018, 06:14 PM RE: New guy and programming problem - Albert Chan - 09-02-2018, 09:21 PM RE: New guy and programming problem - sasa - 09-01-2018, 03:18 PM RE: New guy and programming problem - Albert Chan - 09-01-2018, 05:20 PM RE: New guy and programming problem - sasa - 09-01-2018, 05:33 PM RE: New guy and programming problem - Thomas Klemm - 09-01-2018, 04:28 PM RE: New guy and programming problem - Thomas Klemm - 09-02-2018 07:33 PM RE: New guy and programming problem - Thomas Klemm - 09-02-2018, 09:33 PM RE: New guy and programming problem - Vtile - 09-02-2018, 09:40 PM RE: New guy and programming problem - Albert Chan - 09-03-2018, 10:32 PM

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