Pi using Python

Question

I am a beginner in Python. I try to evaluate pi in Python Language. I use here the Archimedes method.

My code is:

import math
from decimal import *
getcontext().prec = 50

pi = 0
PolySides = 6
SideLen = 1
Perim = 6
Dia = 2

while PolySides < 10000000000:
    SideLen2 = Decimal(SideLen) / Decimal(2)
    radius_a = Decimal(math.sqrt(1 - SideLen2**2))
    radius_b = Decimal(1) - Decimal(radius_a)
    SideLenNew = Decimal(math.sqrt(SideLen2**2 + radius_b**2))
    PolyCircum = Decimal(PolySides * SideLen)
    pi = PolyCircum / Dia
    print('Polygon Sides:', PolySides, 'Pi = ', pi)
    SideLen = SideLenNew
    PolySides = 2 * PolySides

But for some reason this code prints pi upto 14 decimal places. I cannot understand where I'm losing precision. Thank you.

Interesting question. However, it might fit better on codereview. — Mathieu
– Mathieu, Commented Aug 29, 2018 at 11:16
@Mathieu Since the code does not yet work as intended, no, it does not fit better on Code Review. — Mast
– Mast, Commented Aug 29, 2018 at 11:17
I can't reproduce, using your code as-is I am getting a value of pi 49 decimal places long. — Zinki
– Zinki, Commented Aug 29, 2018 at 11:19
@Zinki...My code returns pi =3.1415926535897942262209880937007255852222442626953......which is actually right upto 14 Decimal places — sigma
– sigma, Commented Aug 29, 2018 at 11:21
@IndrajitGhosh ah well that might just be up to floating point arithmetic. standard Floating point types only have 53 bits of precision, which comes out to around 14-15 decimal places. — Zinki
– Zinki, Commented Aug 29, 2018 at 11:22

Amadan · Accepted Answer · 2018-08-29 11:32:50Z

5

You are weaving in and out between float and decimal. math.sqrt takes a float and returns a float, so there'll be conversion where your precision is truncated to float's.

These changes suffice:

while PolySides < 10000000000000000000:
    SideLen2 = Decimal(SideLen) / 2
    radius_a = (1 - SideLen2**2).sqrt()
    radius_b = 1 - radius_a
    SideLenNew = (SideLen2**2 + radius_b**2).sqrt()
    PolyCircum = Decimal(PolySides * SideLen)
    pi = PolyCircum / Dia
    print('Polygon Sides:', PolySides, 'Pi = ', pi)
    SideLen = SideLenNew
    PolySides = 2 * PolySides

edited Aug 29, 2018 at 11:32

answered Aug 29, 2018 at 11:24

Amadan

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2 Comments

unutbu Over a year ago

@IndrajitGhosh: You could use Decimal's sqrt method to fix this problem.

sigma Over a year ago

@unutbu...Thank you ...It fixes my problem.

Thierry Lathuille · Accepted Answer · 2018-08-29 11:30:08Z

2

You must use the .sqrt() method of your decimals:

from decimal import *
getcontext().prec = 50

pi = 0
PolySides = 6
SideLen = 1
Perim = 6
Dia = 2

while PolySides < 1000000000000:
    SideLen2 = Decimal(SideLen) / Decimal(2)
    radius_a = (1 - SideLen2**2).sqrt()
    radius_b = Decimal(1) - Decimal(radius_a)
    SideLenNew = (SideLen2**2 + radius_b**2).sqrt()
    PolyCircum = Decimal(PolySides * SideLen)
    pi = PolyCircum / Dia
    print('Polygon Sides:', PolySides, 'Pi = ', pi)
    SideLen = SideLenNew
    PolySides = 2 * PolySides

Output:

Polygon Sides: 824633720832 Pi =  3.1415926535897932384626357839340399511415560167917

has 22 exact decimals.

answered Aug 29, 2018 at 11:30

Thierry Lathuille

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Comments

damienfrancois · Accepted Answer · 2018-08-29 11:30:42Z

Make sure the variable pi is itself a Decimal too, and avoid using math.sqrt() as @Amadan wrote. Use Decimal.sqrt()

import math
from decimal import *
getcontext().prec = 50

pi = Decimal(0)
PolySides = 6
SideLen = 1
Perim = 6
Dia = 2

while PolySides < 10000000000:
    SideLen2 = Decimal(SideLen) / Decimal(2)
    radius_a = Decimal((Decimal(1) - SideLen2**2).sqrt())
    radius_b = Decimal(1) - Decimal(radius_a)
    SideLenNew = Decimal((SideLen2**2 + radius_b**2).sqrt())
    PolyCircum = Decimal(PolySides * SideLen)
    pi = PolyCircum / Dia
    print('Polygon Sides:', PolySides, 'Pi = ', pi)
    SideLen = SideLenNew
    PolySides = 2 * PolySides

Gives:

Polygon Sides: 6 Pi =  3
Polygon Sides: 12 Pi =  3.1058285412302491481867860514885799401888268158392
Polygon Sides: 24 Pi =  3.1326286132812381971617494694917362446497769154815
Polygon Sides: 48 Pi =  3.1393502030468672071351468212084211891503505893626
Polygon Sides: 96 Pi =  3.1410319508905096381113529264596601070364122161628
Polygon Sides: 192 Pi =  3.1414524722854620754506093089612256452476623045496
Polygon Sides: 384 Pi =  3.1415576079118576455164633451298595415043764795884
Polygon Sides: 768 Pi =  3.1415838921483184086689696037211533505200449157810
Polygon Sides: 1536 Pi =  3.1415904632280500957384585059309517235542823086758
Polygon Sides: 3072 Pi =  3.1415921059992715505447766406101173531274972549662
Polygon Sides: 6144 Pi =  3.1415925166921574475928740847688319059677188923680
Polygon Sides: 12288 Pi =  3.1415926193653839551895493120653190422221927255946
Polygon Sides: 24576 Pi =  3.1415926450336908966721415089192384127226230112419
Polygon Sides: 49152 Pi =  3.1415926514507676517042536404922190204484274723852
Polygon Sides: 98304 Pi =  3.1415926530550368416911231804154742022572768058866
Polygon Sides: 196608 Pi =  3.1415926534561041392646431596150783313543414874292
Polygon Sides: 393216 Pi =  3.1415926535563709636628233165541133642749135041839
Polygon Sides: 786432 Pi =  3.1415926535814376697626683659225751788703495073714
Polygon Sides: 1572864 Pi =  3.1415926535877043462876483788980471857502408672475
Polygon Sides: 3145728 Pi =  3.1415926535892710154188945540564999738004063788314
Polygon Sides: 6291456 Pi =  3.1415926535896626827017061710907747199859793791592
Polygon Sides: 12582912 Pi =  3.1415926535897605995224090799271347533561151459628
Polygon Sides: 25165824 Pi =  3.1415926535897850787275848074223367208751396830886
Polygon Sides: 50331648 Pi =  3.1415926535897911985288787393140192102034265840860
Polygon Sides: 100663296 Pi =  3.1415926535897927284792022222880574573760314838880
Polygon Sides: 201326592 Pi =  3.1415926535897931109667830930316368707217160322736
Polygon Sides: 402653184 Pi =  3.1415926535897932065886783107175360897801705020852
Polygon Sides: 805306368 Pi =  3.1415926535897932304941521151390111674024112028327
Polygon Sides: 1610612736 Pi =  3.1415926535897932364705205662443799538615730707255
Polygon Sides: 3221225472 Pi =  3.1415926535897932379646126790207221515422136434928
Polygon Sides: 6442450944 Pi =  3.1415926535897932383381357072148077010289894182968

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