The Difference of Two Squares

See more James Grime over on Singing Banana.

He is also on some channel called Numberphile.

We have some teacher notes and activity resources for this video on Think Maths. See if your students can find a better graphical proof for the case of 4k than we did! Spoiler: there is one.

CORRECTIONS
- Nothing yet. Let me know if you spot anything!

Thanks to my Patreon supports who do support these videos and make them possible. Here is a random subset:

Daniel Brahneborg
Jan Strohbeck
Marcel de Jong
Thomas Kristian Hodnemyr
Linus Törnqvist

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Music by Howard Carter
Filming and editing by Matt Parker
Design by Simon Wright
Some maths by James Grime.

MATT PARKER: Stand-up Mathematician

[quantummaniac]

If one can't be a prime, why should zero get to be a square?

[matthewsmith]

Most ambitious crossover event in history.

[rachelpoole]

This video has:
A difference of two squares (math)
A difference of two squares (they're on different squares)
A difference of two squares (disagreement between nerds)

[schefre]

Matt and James? This has to be a great video.

[skandragon]

Parker square: not quite right
Grimes square: algebraically precise

[JackKanutin]

I'm slightly annoyed Squarespace didn't sponsor this video....

[ReedHarston]

This Numberphile: Civil War trailer was brilliant. Definitely going to watch this one in theaters. 👍

[blemishingbohemian]

I like how they based an entire video on a pun while actually backing it up with an interesting demonstration about two different types of proof

[aguti]

It's just adorable seeing them walk through London arguing about whether 0 is a square number 😃

[blackpenredpen]

Wow this is such a fun video!! Love the editing and the math!

[SteveMould]

James is right. I won't get out of bed for less than £(a² - b²).

[clf]

Loving the Leicester Square and Trafalgar Square backgrounds

[tone]

I'm with James on this one: 0's an integer, and squaring an integer gets you a square number, so 0^2 is a square number.

[ShinySwalot]

"I am cheaper than Steve Mould"
I'm dying, I love these two

[xalkin]

at Leicester Square and Trafalgar Square talking about different Squares...brilliant :)

[AnonymousFreakYT]

The difference of two squares? With Matt & James?

Let's see... James has more hair. Matt has a goofier accent.

[AceMartinov]

Video length should have been 9:16 for two squares, missed opportunity

[ze_rubenator]

Oh right, and you're standing on different "squares" as you're explaining. Well played, good sirs!

[dirm]

Bring back the old public maths offs! Love this format.

[stevepalmer]

Ha ha! Who else spotted the kid's super smooth wall dismount at 5:45?