Tutorial: Fibonacci numbers start with 1, 1

[skyhein]

BPO	31757
Nosy	@rhettinger, @terryjreedy, @mdickinson, @stevendaprano
PRs	bpo-31757: Make Fibonacci examples consistent #3991

^{Note: these values reflect the state of the issue at the time it was migrated and might not reflect the current state.}

Show more details

GitHub fields:

assignee = 'https://github.com/rhettinger'
closed_at = <Date 2017-10-14.14:36:58.087>
created_at = <Date 2017-10-11.14:40:19.957>
labels = ['type-bug', '3.7', 'docs']
title = 'Tutorial: Fibonacci numbers start with 1, 1'
updated_at = <Date 2017-10-14.14:36:58.087>
user = 'https://bugs.python.org/skyhein'

bugs.python.org fields:

activity = <Date 2017-10-14.14:36:58.087>
actor = 'rhettinger'
assignee = 'rhettinger'
closed = True
closed_date = <Date 2017-10-14.14:36:58.087>
closer = 'rhettinger'
components = ['Documentation']
creation = <Date 2017-10-11.14:40:19.957>
creator = 'skyhein'
dependencies = []
files = []
hgrepos = []
issue_num = 31757
keywords = ['patch']
message_count = 8.0
messages = ['304144', '304156', '304157', '304167', '304174', '304363', '304375', '304394']
nosy_count = 6.0
nosy_names = ['rhettinger', 'terry.reedy', 'mark.dickinson', 'steven.daprano', 'docs@python', 'skyhein']
pr_nums = ['3991']
priority = 'normal'
resolution = 'fixed'
stage = 'resolved'
status = 'closed'
superseder = None
type = 'behavior'
url = 'https://bugs.python.org/issue31757'
versions = ['Python 3.7']

[skyhein]

In https://docs.python.org/3/tutorial/controlflow.html#defining-functions both examples produce fibonacci numbers starting with 0. They should start with 1, as in the example in https://docs.python.org/3/tutorial/introduction.html#first-steps-towards-programming

The first example should change the lines
while a < n:
print(a, end=' ')
to
while b < n:
print(b, end=' ')

and the second example should change the lines
while a < n:
result.append(a) # see below
to
while b < n:
result.append(b) # see below

[mdickinson]

Is there any particular reason you want to start with 1? While not universal, it's standard to define Fib(0) = 0, and to start the sequence at 0. (And note that Python usually starts indexing things from 0, so it makes sense to start with Fib(0) rather than Fib(1).)

In principle, one could define Fib(0)=1, Fib(1)=1, Fib(1)=2, and so on, but there's a strong reason not to do so: it breaks (or at least uglifies) many nice number-theoretic properties, like gcd(Fib(m), Fib(n)) == Fib(gcd(m, n)).

[mdickinson]

A nice response to the question of whether to start with 0 or 1 here: https://stackoverflow.com/a/5901955

The definition with Fib(0) = 1 is known as the combinatorial
definition, and Fib(0) = 0 is the classical definition. Both
are used in the Fibonacci Quarterly, though authors that use
the combinatorial definition need to add a sentence of
explanation.

I confess that I hadn't heard of the Fibonacci Quarterly before.

[skyhein]

I would not insist of starting with 1 instead of 0 (I follow your arguments here), but perhaps it would be nice if it would behave the same way in both chapters. The first fibonacci number examples in https://docs.python.org/3/tutorial/introduction.html#first-steps-towards-programming start with 1.

There are three examples here, in the first,

while b < 10:
    print(b)

should change to

while a < 10:
    print(a)

The output of this first example would have an additional 0:
0
1
1
...

And in the third example

while b < 1000:
    print(b, end=',')

should change to

while a < 1000:
    print(a, end=',')

where the output of this third example would change from

1,1,2,3,5,8,13,21,34,55,89,144,233,377,610,987,

to

0,1,1,2,3,5,8,13,21,34,55,89,144,233,377,610,987,

[mdickinson]

I agree it would be good to be consistent.

[terryjreedy]

I agree that we should be consistent -- with the current standard definition -- with the changes suggested above. Heinrich, can you, and do you want to, submit a patch? If so, please also sign the contributor agreement. See https://www.python.org/psf/contrib/

The Fibonacci numbers start with 1 if there is no F(0), as in Fibonacci's rabbit model. Before 0 was accepted as a number, the series had to start with F(1) = F(2) = 1. See https://en.wikipedia.org/wiki/Fibonacci_number

[rhettinger]

I update the example in "First Steps Towards Programming" to match the one in "Defining Functions" (which is also shown on the home page at www.python.org.

[rhettinger]

New changeset 8c26a34 by Raymond Hettinger in branch 'master':
bpo-31757: Make Fibonacci examples consistent (bpo-3991)
8c26a34