Musings on the HP-70
12-29-2023, 10:35 AM (This post was last modified: 12-30-2023 08:47 AM by Thomas Klemm.)
Post: #1
 Thomas Klemm Senior Member Posts: 2,071 Joined: Dec 2013
Musings on the HP-70

Fibonacci Sequence

Initialisation

DSP 0
CLR
STO M
1

Loop

M+
x<>y

Result

0.
1.
1.
2.
3.
5.
8.
13.
21.
34.

Explanation

\begin{aligned} x_{0} &= 0 \\ x_{1} &= 1 \\ \\ x_{n+1} &= x_{n} + x_{n-1} \\ \end{aligned}

Python Program

Code:
a, b = 0, 1 for k in range(10):     print(a)     a, b = b, a + b

References

Viète's formula for $$\pi$$

Initialisation

DSP 9
0.5
STO K
CLR
STO M
2
ENTER
ENTER
ENTER

Loop

x<>y
M+
K
yx
STO M
÷
×

Result

2.000000000
2.828427125
3.061467459
3.121445152
3.136548491
3.140331157
3.141277251
3.141513801
3.141572940
3.141587725
3.141591422
3.141592346
3.141592577
3.141592634
3.141592649
3.141592652
3.141592653
3.141592654
3.141592654

Explanation

$$\pi = 2 \cdot \frac{2}{\sqrt{2}} \cdot \frac{2}{\sqrt{2 + \sqrt{2}}} \cdot \frac{2}{\sqrt{2 + \sqrt{2 + \sqrt{2}}}} \cdots$$

Python Program

Code:
from math import sqrt p, q = 2, 0 for k in range(20):     print(f"{p:>.9f}")     q = sqrt(2 + q)     p *= 2 / q

References

• Can you guess the result?
• Can you come up with other interesting recipes?
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 Messages In This Thread Musings on the HP-70 - Thomas Klemm - 12-29-2023 10:35 AM RE: Musings on the HP-70 - Thomas Klemm - 12-29-2023, 12:53 PM RE: Musings on the HP-70 - Thomas Klemm - 12-30-2023, 09:02 AM