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.
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.
https://users.mccme.ru/akopyan/papers/EnGeoFigures.pdf
Caution: proofs of some of the statements in it are difficult.
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.