Sharp EL-512: Lorentz Factor, Table, Geometric Mean, 3D Vectors
Blog entries now made in Windows 11.
Today’s blog will feature the classic Sharp EL-512 from the 1980s. The Sharp EL-512 is a keystroke programming calculator. The EL-512 has four program slots with a memory of 128 programming steps. All programs on the EL-512 are “entered in the blind” and must be entered in full each time.
Program commands:
[ x ]: prompt for a number. When editing a program, we will need to enter a valid number to continue the program.
LOOK: Stops the program and shows the immediate results.
Memory and recall:
STO: Stores the number in the display to memory register 1-9
x → M: Store the number in the display to memory M
M+: add to memory M
RM: recall memory M
Kn:
After a clear or an arithmetic key, just recalls the contents of memory register 1-9.
After entering a number, multiplies the number in the display by the contents of the memory register 1-9 (like RCL× K#)
To recall a register without alteration, it is always safe to multiply the register by 1:
1 Kn #
My review from 2020:
https://edspi31415.blogspot.com/2020/09/retro-review-sharp-el-512-scientific.html
Lorenz Factor
LF = (√(1-v²/c²))⁻¹
c = Speed of light in a vacuum = 299,792,452 m/s
Program:
x²
÷
299792458
x²
+/-
1
=
√
1/x
Examples:
v = 2.1E8 (2.1 * 10^8) m/s; Result: 1.401212716
v = 2,456,000 m/s; Result: 1.000033559
v = 1,000,000 m/s; Result: 1.060752
Table: Quadratic Polynomial
Generate a table using the function:
f(x) = K3 × x² + K2 × x + K1
where x increases by 1.
Before running the program, store the following:
x² coefficient: K3
x coefficient: K2
constant coefficient: K1
beginning value: Subtract 1, then store the starting value in M. For example, if we want to start with x = 1, store 0 in M.
Program:
1
M+
RM
x²
Kn 3
+
RM
Kn 2
+
1
Kn 1
=
Example:
f(x) = 0.3 × x² + 4 × x – 2.01
Start with x = 1
0.3 STO 3
4 STO 2
-2.01 STO 1
1-1 = 0 x→M
Run the program:
f(1) = 2.29
f(2) = 7.19
f(3) = 12.69
f(4) = 18.79
f(5) = 25.49
Geometric Mean
This program calculates the geometric mean (Π(x_i)^(1/n)) by the formula:
GM = 1/n × Σ(ln x_i) (x≠0)
This will require two program slots, so I’m using program slots 1: and 2:.
Memory registers used:
K1 = Σ(ln x_i)
M = n
Steps:
1. Store 0 to memory M (x→M) and memory 1 (STO 1)
2. Enter x_i and press 1:. Continue until you enter all the data. The number of data points is shown.
3. Press 2: to get the geometric mean.
Program 1:
ENT (enter a valid number)
LN
+
Kn 1
=
STO 1
1
M+
RM
Program 2:
RM
1/x
Kn 1
e^x
Example:
Find the geometric mean of 4, 9, 3, 7, 2, 8, 8, 5, and 6. 9 data points.
0 x→M, 0 STO 1
4 [1:], 9 [1:], 3 [1:], 7 [1:], 2 [1:], 8 [1:], 8 [1:], 5 [1:], 6 [1:]
[2:]
Result (geometric mean): 5.2254102087
3D Vectors: Norm of Two Vectors, Dot Product, Angle between Vectors
For this, I presume that the calculator is set to the desired angle setting (DRG). For the example, I have the EL-512 set to degree mode.
Store the vectors as follows:
First vector: [ register 1, register 2, register 3 ]
Second vector: [ register 4, register 5, register 6 ]
The program returns four values:
Norm of the first vector, stored in register 7
Norm of the second vector, stored in register 8
Dot product, stored in registered in M
Angle between two vectors, stored in register 9
Program:
1
Kn 1
↕
1
Kn 2
→rθ
↕
1
Kn 3
→rθ
STO 7
LOOK
1
Kn 4
↕
1
Kn 5
→rθ
↕
1
Kn 6
→rθ
STO 8
LOOK
1
Kn 1
Kn 4
x→M
1
Kn 2
Kn 5
M+
1
Kn 3
Kn 6
M+
RM
LOOK
÷
(
1
Kn 7
Kn 8
)
=
cos⁻¹
STO 9
Example:
First vector: [ 70, 64, 36 ]
Second vector: [ 55, 18, 94 ]
Results:
Norm of first vector: 101.4494948
Norm of second vector: 110.3856875
Dot product: 8386
Angle: 41.50953299°
Hope you enjoyed this trip down memory lane. Did you have or do you have a Sharp EL-512 or any similar calculator?
Eddie
All original content copyright, © 2011-2025. Edward Shore. Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited. This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author.
