TI-60: Triangle Numbers
12-19-2018, 04:23 AM
Post: #6
 Thomas Klemm Senior Member Posts: 1,447 Joined: Dec 2013
RE: TI-60: Triangle Numbers
(12-16-2018 05:33 PM)Dieter Wrote:  This is essentially a "proof of concept" on how to do loops on a calculator with an extremely limited function set without tests and goto

We could exploit the integration key and do some calculations in a loop as a side effect.
This allows to implement a solver using fixed point iteration or Newton's method.
However you could specify only up to 99 loops.

To solve Kepler's equation:

$$M = E - e \sin E$$

We would rewrite it as a fixed point equation:

$$E = M + e \sin E$$

Using the following mapping to the data memories:

E: 3
M: 4
e: 5

We could then use this program:
Code:
RCL 4 + RCL 5 × RCL 3 sin = STO 3

We don't really care about the lower and upper limits of the interval so we could just use:

0 STO 1
1 STO 2

The integration would be started with:

∫dx nn R/S

The result could then be found in register 3.

Using realistic values (e.g. e = 0.0167 for the Earth) this needs only a few iterations.
Don't forget to put the calculator into the radian mode.

Cheers
Thomas
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 Messages In This Thread TI-60: Triangle Numbers - Eddie W. Shore - 12-16-2018, 03:35 AM RE: TI-60: Triangle Numbers - Dieter - 12-16-2018, 05:33 PM RE: TI-60: Triangle Numbers - grsbanks - 12-16-2018, 07:08 PM RE: TI-60: Triangle Numbers - Thomas Klemm - 12-16-2018, 09:56 PM RE: TI-60: Triangle Numbers - ijabbott - 12-17-2018, 02:55 PM RE: TI-60: Triangle Numbers - Thomas Klemm - 12-19-2018 04:23 AM

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