+- HP Forums (https://www.hpmuseum.org/forum)
+-- Forum: Not HP Calculators (/forum-7.html)
+--- Forum: Not remotely HP Calculators (/forum-9.html)
+--- Thread: TI-60: Triangle Numbers (/thread-11956.html)
TI-60: Triangle Numbers - Eddie W. Shore - 12-16-2018 03:35 AM
Here I exploit TI-60'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).
TI-60 Program: Triangle Numbers
Code:
PC00 OP71: RCL
PC01 OP01: 1
PC02 OP61: STO
PC03 OP85: +
PC04 OP00: 0 // sum R1 in R0
PC05 OP75: -
PC06 OP01: 1
PC07 OP95: =
PC08 OP61: STO
PC09 OP01: 1 // store R1 -1 in R1
PC10 OP86: √ // take the square root of R1, if R1<0, the error occurs, ending the "loop"
PC11 OP22: RST // reset back to step 00Link to blog post: https://edspi31415.blogspot.com/2018/12/ti-60-triangle-numbers.html
RE: TI-60: Triangle Numbers - Dieter - 12-16-2018 05:33 PM
(12-16-2018 03:35 AM)Eddie W. Shore Wrote: Here I exploit TI-60'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 TI-60 "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
RE: TI-60: Triangle Numbers - grsbanks - 12-16-2018 07:08 PM
(12-16-2018 03:35 AM)Eddie W. Shore Wrote: Here I exploit TI-60's RST function's ability to continue program execution
Such a pain in the rear end that the TI-56 (and presumably the TI-55III) halt execution before resetting the program counter making it impossible to program loops of any kind! Even the prehistoric TI-53 does it "right"
RE: TI-60: Triangle Numbers - Thomas Klemm - 12-16-2018 09:56 PM
(12-16-2018 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 TI-60 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:
+
1.002
=
nCrCheers
Thomas
RE: TI-60: Triangle Numbers - ijabbott - 12-17-2018 02:55 PM
(12-16-2018 09:56 PM)Thomas Klemm Wrote:(12-16-2018 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 TI-60 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:
+
1.002
=
nCr
Cheers
Thomas
Using the formula saves a couple of program steps (assuming there are no pending operations before running the program):
Code:
+
x²
=
÷
2
=RE: TI-60: Triangle Numbers - Thomas Klemm - 12-19-2018 04:23 AM
(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 3We 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