NHacker Next
login
▲Proofs Without Wordsartofproblemsolving.com
41 points by squircle 4 days ago | 11 comments
Loading comments...
cuber_messenger 2 hours ago [-]
There's a book called "Proofs without words". Fun to have a glance. (https://ia801405.us.archive.org/24/items/proofs-without-word...) It also has a sequel.
fiforpg 6 hours ago [-]
Nice. There's an entire book like this for geometric statements. Every picture is a fact, proofs are supplied by the reader:

https://users.mccme.ru/akopyan/papers/EnGeoFigures.pdf

Caution: proofs of some of the statements in it are difficult.

JadeNB 5 hours ago [-]
I think that is rather different. The traditional meaning of "proofs without words" is that the picture is the proof, or at least, if you believe that a proof can only be in words, that the picture should convey the idea so transparently that anyone with reasonable mathematical skill can routinely translate it into words.
vismit2000 5 hours ago [-]
There is also this youtube channel called 'Mathematical Visual Proofs' on similar theme: https://www.youtube.com/@MathVisualProofs
ViscountPenguin 2 hours ago [-]
I've never really been a fan of proofs without words; they've always felt way too slippery to me, for lack of a better term. A well worded proof with nice explanatory diagrams hits the spot for me instead.
perlgeek 30 minutes ago [-]
For me, the visual proofs of simple sums (like The sum of the first n odd natural numbers is n²) works pretty well for me.

For the more geometry-based ones where you have move triangles around and so, it's often not obvious to me that two angles that look the same really always are the same, and that things that add up to rectangle do so reliably, independently of the actual angles used in the examples.

I guess in these cases, a more parameterized, interactive version would work better, where you can use sliders to adjust some of the angles and lengths used. That should make it much more obvious that it's not just an artifact of particular angles used in an example.

paufernandez 59 minutes ago [-]
I'm the opposite. I am not convinced until I "see it". Probably has to do with our innate talents.
downboots 5 hours ago [-]
Another great site is https://theoremoftheday.org/ with a neat one-pager overview of each theorem
vonnik 5 hours ago [-]
Anyone who enjoys this should read David Bessis’s Mathematica.
jupitr 3 hours ago [-]
and also how to lie with visual proofs: https://www.youtube.com/watch?v=VYQVlVoWoPY
brianberns 5 hours ago [-]
I made a game out of creating proofs without words: https://brianberns.github.io/Tactix/