TI60: Triangle Numbers

12162018, 03:35 AM
Post: #1




TI60: Triangle Numbers
Here I exploit TI60's RST function's ability to continue program execution and using the square root function as a "tester" to calculate triangle numbers.
Instructions: 1. In RUN mode (outside of LRN), store the following values: R0 = 0 R1 = n 2. Execute the program by pressing [RST], [R/S]. The program is done when you see "Error". 3. Clear the error by pressing [CE/C]. 4. Recall R0. This is your triangle number. (R1 will have 1). TI60 Program: Triangle Numbers Code:
Link to blog post: https://edspi31415.blogspot.com/2018/12/...mbers.html 

12162018, 05:33 PM
Post: #2




RE: TI60: Triangle Numbers
(12162018 03:35 AM)Eddie W. Shore Wrote: Here I exploit TI60's RST function's ability to continue program execution and using the square root function as a "tester" to calculate triangle numbers. 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 – rskey.org calls the TI60 "almost programmable". ;) In real life, if you want the sum of all integers from 1 to n you'd of course use the direct formula ½n(n+1) or ½(n²+n). Less steps, direct result. Dieter 

12162018, 07:08 PM
Post: #3




RE: TI60: Triangle Numbers
(12162018 03:35 AM)Eddie W. Shore Wrote: Here I exploit TI60's RST function's ability to continue program execution Such a pain in the rear end that the TI56 (and presumably the TI55III) halt execution before resetting the program counter making it impossible to program loops of any kind! Even the prehistoric TI53 does it "right" 

12162018, 09:56 PM
Post: #4




RE: TI60: Triangle Numbers
(12162018 05:33 PM)Dieter Wrote: In real life, if you want the sum of all integers from 1 to n you'd of course use the direct formula ½n(n+1) or ½(n²+n). Less steps, direct result. The TI60 provides an nCr key with a bit weird usage: Quote:The values of n and r are entered as n.rrr. Thus we could use: Code: + Cheers Thomas 

12172018, 02:55 PM
(This post was last modified: 12172018 02:56 PM by ijabbott.)
Post: #5




RE: TI60: Triangle Numbers
(12162018 09:56 PM)Thomas Klemm Wrote:(12162018 05:33 PM)Dieter Wrote: In real life, if you want the sum of all integers from 1 to n you'd of course use the direct formula ½n(n+1) or ½(n²+n). Less steps, direct result. Using the formula saves a couple of program steps (assuming there are no pending operations before running the program): Code: + — Ian Abbott 

12192018, 04:23 AM
Post: #6




RE: TI60: Triangle Numbers
(12162018 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 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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