4 ms·

According to my numerical computing classes the best value of PI on your computing platform is: atan(1.0) * 4 And if there's no math package on your system al

According to my numerical computing classes the best value of PI on your computing platform is: atan(1.0) * 4 And if there's no math package on your system already defining PI then that's the value you should use - assuming there aren't legal requirements mandating other values to be used instead.

daveFNbuck 6y ago
Are there a lot of systems that define arctangent but not pi?
- gandalf013 6y ago
  bc calculator doesn't (or didn't) define pi, but has atan. I've used "4*atan(1) method" in bc to get pi.
  - ape4 6y ago
    This works, `echo 'scale=100;4*a(1)' | bc -lq`
- kens 6y ago
  The cheap Sinclair Scientific calculator (1974) was rather primitive, so instead of storing constants internally, it printed constants such as e and pi on the case. The calculator was rather inaccurate, so you were much better off using 3.14159 from the case than computing 4×atan(1), which gave 3.1440.
  - taylodl 6y ago
    It'd be interesting to see their implementation and the trade-offs its designers made.
    - kens 6y ago
      I'm glad you asked :-) I reverse-engineered the Sinclair Scientific calculator, documented its code, and built a simulator: http://files.righto.com/calculator/sinclair_scientific_simulator.html http://files.righto.com/calculator/sinclair_scientific_simul... The short answer is that they used a 4-function calculator chip with just 320 words of ROM and managed to reprogram it into a cheap scientific calculator, a remarkable feat. The tradeoff was that the calculator was very slow and inaccurate.
      - taylodl 6y ago
        That's amazing! Thank you for sharing!
- taylodl 6y ago
  C/C++ don't define PI but have an atan function. According to the TIOBE Index for September 2020 (https://www.tiobe.com/tiobe-index/ https://www.tiobe.com/tiobe-index/) those languages are both in the top 5 of languages used by developers.
  - votepaunchy 6y ago
    C++20 defines mathematical constants including Pi. https://en.cppreference.com/w/cpp/numeric/constants https://en.cppreference.com/w/cpp/numeric/constants
    - taylodl 6y ago
      Thanks for the heads up! I haven't been paying any attention to C++20. You must be on the cutting edge of C++ to know that - I ended up having to work a bit on my Macbook Pro to get a version of gcc working that defines std::numbers::pi.
  - saagarjha 6y ago
    They don’t but POSIX requires M_PI.
- xioxox 6y ago
  Yes - Fortan doesn't have a built-in pi constant, but does have trigonometric functions. Usually programs define pi based on atan or some other trig relation.
srathi 6y ago
I assume the later part of you comment refers to the (in)famous attempt by the Indiana state assembly to legalize Pi to be exactly equal to 3.
- taylodl 6y ago
  That thought had come across my mind, but no, I've seen engineering requirements stating something to the effect that the value of PI used in these calculations is to be 3.1415, for example.
deleted 6y ago
[deleted]

daveFNbuck 6y ago

Are there a lot of systems that define arctangent but not pi?

gandalf013 6y ago
bc calculator doesn't (or didn't) define pi, but has atan. I've used "4*atan(1) method" in bc to get pi.
- ape4 6y ago
  This works, `echo 'scale=100;4*a(1)' | bc -lq`
kens 6y ago
The cheap Sinclair Scientific calculator (1974) was rather primitive, so instead of storing constants internally, it printed constants such as e and pi on the case. The calculator was rather inaccurate, so you were much better off using 3.14159 from the case than computing 4×atan(1), which gave 3.1440.
- taylodl 6y ago
  It'd be interesting to see their implementation and the trade-offs its designers made.
  - kens 6y ago
    I'm glad you asked :-) I reverse-engineered the Sinclair Scientific calculator, documented its code, and built a simulator: http://files.righto.com/calculator/sinclair_scientific_simulator.html http://files.righto.com/calculator/sinclair_scientific_simul... The short answer is that they used a 4-function calculator chip with just 320 words of ROM and managed to reprogram it into a cheap scientific calculator, a remarkable feat. The tradeoff was that the calculator was very slow and inaccurate.
    - taylodl 6y ago
      That's amazing! Thank you for sharing!
taylodl 6y ago
C/C++ don't define PI but have an atan function. According to the TIOBE Index for September 2020 (https://www.tiobe.com/tiobe-index/ https://www.tiobe.com/tiobe-index/) those languages are both in the top 5 of languages used by developers.
- votepaunchy 6y ago
  C++20 defines mathematical constants including Pi. https://en.cppreference.com/w/cpp/numeric/constants https://en.cppreference.com/w/cpp/numeric/constants
  - taylodl 6y ago
    Thanks for the heads up! I haven't been paying any attention to C++20. You must be on the cutting edge of C++ to know that - I ended up having to work a bit on my Macbook Pro to get a version of gcc working that defines std::numbers::pi.
- saagarjha 6y ago
  They don’t but POSIX requires M_PI.
xioxox 6y ago
Yes - Fortan doesn't have a built-in pi constant, but does have trigonometric functions. Usually programs define pi based on atan or some other trig relation.

srathi 6y ago

I assume the later part of you comment refers to the (in)famous attempt by the Indiana state assembly to legalize Pi to be exactly equal to 3.

taylodl 6y ago
That thought had come across my mind, but no, I've seen engineering requirements stating something to the effect that the value of PI used in these calculations is to be 3.1415, for example.

deleted 6y ago

[deleted]