Aug 16, 2026, 5:41 AMHave you ever noticed you can calculate the sequence of perfect squares without doing any multiplication
- Aug 16, 2026, 5:41 AM
Replies
- Aug 16, 2026, 5:51 AM
a = 1
b = 3
while True:
print(a)
a = a + b
b = b + 2 
Aug 16, 2026, 5:43 AM@mcc Nope
- Aug 16, 2026, 5:43 AM
@Steve Well, you can
- Aug 16, 2026, 5:44 AM
@mcc I'll take your word for it.
Aug 16, 2026, 5:46 AM@mcc I "discovered" this when learning arithmetic progression in high school
estelleestelle@mstdn.socialAug 16, 2026, 5:54 AM@mcc you're about to hear from some math majors about the very interesting relation between the integral and the summation, it's not my place to explain this well, etc,
Phil Dissonancephilphi@metalhead.clubAug 16, 2026, 5:59 AMIt's clever... I think you are essenrially using
(n+1)² = n² + 2n + 1
where a = n² and b = 2n + 1 ... you are starting at those values for n = 1 and then use it to compute the n = 2 squarw and then since b = 2n + const you have to increase it by 2 in each step
Aug 16, 2026, 6:29 AM
LRlritter@mastodon.gamedev.placeAug 16, 2026, 8:14 AM
Outfrostoutfrost@mastodon.socialAug 16, 2026, 6:31 AM@mcc
sq = 1
n = 0
while True:
print(sq)
n += 1
sq += n + n + 1
mal3abymal3aby@mastodon.smears.orgAug 16, 2026, 7:11 AM@mcc Another similarly pleasing fact is that you can generate all the coordinates needed to plot the boundary of a circle (on a raster display) without trig, square root or even much multiplication.
Aug 16, 2026, 7:37 AM@mcc any multiplication can be replaced by additions in a loop?
Mark Reidmdreid@mastodon.socialAug 16, 2026, 6:16 AM@mcc Using this observation?
Ben Curthoysbencurthoys@mastodon.socialAug 16, 2026, 7:09 AM@mcc get a load of this one:
Robert Hutchinsonertchin@mstdn.socialAug 16, 2026, 7:27 AM@mcc Slightly related: the product of two positive integers that are 2 apart is always exactly one less than the square of the integer in between them.
So you can say with alacrity and confidence that, for instance, the product of 1,999 and 2,001 is 3,999,999.
[ (x+1) * (x-1) = x^2 - 1 ]
[ The difference is in fact always y^2 less when the integers are each y away from the center, so 1,980 * 2,020 = 3,999,600 ]
Nikita Lisitsalisyarus@mastodon.gamedev.placeAug 16, 2026, 8:06 AM@mcc Yep!
John Carlos Baezjohncarlosbaez@mathstodon.xyzAug 16, 2026, 8:54 AM@mcc - I feel anyone who claims to be a mathematician should have thought about this. Plus it's super-fun!
