Curry's Paradox and the Notion of Area: Part I (Tanton)

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DrJamesTanton

DrJamesTanton

13 жыл бұрын

Here is a wonderful paradox due to Paul Curry that challenges our beliefs on how area behaves. In this video I show the paradox, resolve paradox, and then in parts II and III of the video show how I use the paradox in teaching.

Пікірлер: 54
@alchemistforgold3793
@alchemistforgold3793 5 жыл бұрын
Love your explanation of the Curry's paradox!
@MichaPawlickiTenFajny
@MichaPawlickiTenFajny 10 жыл бұрын
Oh thank you for,understanding this!
@tinypeterrabbit
@tinypeterrabbit Жыл бұрын
It is one in the morning but I saw the Curry's Paradox for the first time ever while scrolling Tumblr and needed to know where the extra space was coming from immediately. Thank you so much for the explanation! It's funny that the human brain ignores things (like slight changes in slope) to keep with the larger picture.. I guess that can be said about a lot of things huh? Great video 👍
@EXPLORADVEN
@EXPLORADVEN Жыл бұрын
Awesome Explanation 🙏🙏🙏🙏
@bernardomesilva
@bernardomesilva 11 жыл бұрын
Nice video and good explantion. :)
@aldoraine7848
@aldoraine7848 10 жыл бұрын
Oh man I don´t understand everything, because I am from Germany, but I love it! Nice Video! Thanks for the upload!
@JimGiant
@JimGiant 9 жыл бұрын
The area of the bulge is surely half a square in the other configuration the area of the indent should be half a square so added together they account for the missing square.
@reformandpurify4873
@reformandpurify4873 5 жыл бұрын
Could you make a video of it with cake?
@mafioza24
@mafioza24 13 жыл бұрын
very nice =)
@Capturing-Memories
@Capturing-Memories 9 жыл бұрын
so in geometry the theory that says that two parallel lines crossed by another line in an angle both angles formed by the crossed line and the parallel lines should be perfectly equal, I'm referring to the sharpest angles of both yellow and purple triangles, if those angles are perfectly equal the line formed by those triangles should a straight line in both cases.
@Kaianacoel
@Kaianacoel 11 жыл бұрын
Very very nice video! I knew there was something fishy with the first example, the lines were noticeably not straight :D Less so with the second one, to be honest. Thank you for explaining this paradox. I see your other videos on the right, and I'm going to watch them now :D For !!SCIENCE!!
@SolLederman
@SolLederman 13 жыл бұрын
Nice video. It's also worth exploring how the Fibonacci series is involved in the creation of the paradox.
@joshlara8237
@joshlara8237 2 жыл бұрын
Man this world has stuff that can melt my brain n we haven't ever even been on other planets or know earth 100% yet
@benjamindorsey2058
@benjamindorsey2058 3 жыл бұрын
Thank u!!
@MagicVijayTamil
@MagicVijayTamil 11 жыл бұрын
sir pls send correct measurement for TRIANGLE PUZZLE demonstrated in the first part of this video
@pedrooavz
@pedrooavz 11 жыл бұрын
What could go wrong if I try to do this with chocolate?
@nickmicheli930
@nickmicheli930 10 жыл бұрын
I'm still confused. Even in the first triangle (displayed at 2:50) has a change in the slope partially up the hypotenuse.
@niclasfilms1
@niclasfilms1 3 жыл бұрын
7 years late, but I think the difference in area between the bulge in the second one and the notch in the first one (that kite like form) should have the area of exactly one square unit. That exact difference in area is then seen in the hole in the bottom right
@GUISCHOL
@GUISCHOL 3 жыл бұрын
Wow, das ist wirklich colle MATHEMATIK. In der Antike war Rechnen und Geometrie stark miteinander verbunden. Hätten die alten Griechen ein Problem mit diesem Video gehabt? Wow, that's really cool MATHEMATICS. In ancient times, arithmetic and geometry were strongly connected. Would the ancient Greeks have had a problem with this video?
@StefanTravis
@StefanTravis 8 жыл бұрын
So this would be a _visual_ falsidical paradox. One where the obscured error isn't in ambiguous terms, division by zero, unstated premises etc., but in how we look at diagrams.
@KanoBoom
@KanoBoom 4 жыл бұрын
Notice how the length form a fibonacci sequence
@mathpro01
@mathpro01 9 жыл бұрын
See the remark by Sol Lederman.
@Bilanski
@Bilanski 3 жыл бұрын
Can someone explain, how we come on 3/5 hypotenuse? I used The Pythagorean Theorem and didn't come on the same answer. Pls , my brains need information.
@Bilanski
@Bilanski 3 жыл бұрын
A2+B2=C2 (2^2+5^2)^1/2=hypontenus
@Bilanski
@Bilanski 3 жыл бұрын
5.38516480713
@Cyberdactyl
@Cyberdactyl 10 жыл бұрын
It is close, but not quite, as bizarre as the Monty Hall 3 Door Problem.
@dangar52
@dangar52 4 жыл бұрын
Paul Curry is a magician. I have read that Curry's Paradox is attributed to logician Haskell Curry, NOT Paul. What is your source for this?
@mandebo
@mandebo 2 жыл бұрын
Different paradox and different Curry
@straightwhiteman755
@straightwhiteman755 10 жыл бұрын
Did you watch the video? He explained it very clearly lol...
@guitardude125
@guitardude125 7 жыл бұрын
merely an illusion. the slope of the two triangles are not equal. You can see the convexity and concavity between the two arranged shapes. that is where the "missing" area is
@MyTimelord11
@MyTimelord11 6 жыл бұрын
Peyton Wilson you can see they are. He used dots to show that the angles are the same both times.
@user-hl4yk3vf6q
@user-hl4yk3vf6q 11 жыл бұрын
that is funnnnny
@QueueWithACapitalQ
@QueueWithACapitalQ 4 жыл бұрын
I noticed the first triangle bulged but didn’t think anything of it
@terrycook5878
@terrycook5878 9 жыл бұрын
QI brought me here. Stephen Fry tricks you into learning.
@gurdatsingh6274
@gurdatsingh6274 3 жыл бұрын
I want to make the puzzle but I am failing every time
@stvltiloqvent
@stvltiloqvent 10 жыл бұрын
if your heart is a triangle
@saedabumokh9577
@saedabumokh9577 9 жыл бұрын
see 0:14 then immediately see 1 :45
@mexicaniggy169
@mexicaniggy169 11 жыл бұрын
paused video just after 1:27 , rode my bike to Carvel, bought a cookie puss, sped home, cut into proper triangle, as shown above, unpause..... 3:41 >8O . A part of me still holds out hope for Fudgie the whale.
@tomtomspa
@tomtomspa 10 жыл бұрын
the area you underline, is not 1 unit squared, it is half unit squared!
@mudchair16
@mudchair16 11 жыл бұрын
Sorcery. He shall burn.
@glenarth
@glenarth 9 жыл бұрын
i wish i was high on potenuse
@booni5114
@booni5114 9 жыл бұрын
glenarth Key & Peele
@stza16
@stza16 8 жыл бұрын
+glenarth I am so high on potenuse right now.
@MyTimelord11
@MyTimelord11 6 жыл бұрын
I'm stoned. And this was amazing.
@user-dd1um4fh5w
@user-dd1um4fh5w 4 жыл бұрын
0:14 1:45
@mortendahl5552
@mortendahl5552 2 жыл бұрын
Things don't become "paradoxes" just because you are easy to fool
@williswicked
@williswicked 11 жыл бұрын
how the fuck did he do that
@shushilpant7915
@shushilpant7915 3 жыл бұрын
1:45
@aarongoldsmith9967
@aarongoldsmith9967 8 жыл бұрын
I like the paradox. But, area is b*h/2.
@wills8288
@wills8288 8 жыл бұрын
This is deceptive and stupid. Certainly not a paradox.
@petibosco
@petibosco 11 жыл бұрын
stop la branlette, va produire et realiser tes theories avec tes mains..... La pensee, egale et rivale de la main, l'une ne peut rien sans l'autre. Parle en clair de ton idee et de son aboutissement reel et palpable. stop aux palabres et autres performances aproximatives basees sur du papier. bon courage qqmm
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