Sneak Peek at a new video
Added 2023-11-27 22:36:15 +0000 UTCHi everyone,
Can you solve the SAT math question that every test-taker got wrong? Our new video is all about one weird paradox that has impacted everything from SAT exams to astronomy…
As usual, would love to know of any suggestions, confusions, corrections, or thoughts in general. Note some animations and demos are still works in progress.Hope you enjoy, and thanks so much for your support & feedback!
Emily, on behalf of the Ve team.
Comments
People who make clothing are aware of this reality, whether or not they see it as a math problem. The pattern for a collar and its shirt is tricky. Beginners often have to redo the set of the collar because the offset for seam allowance is not intuitive on a curve.
Whitney Wetherill
2024-02-13 02:32:46 +0000 UTCThis actually reminds me a lot of the question of how many times do a clock's hands (minute and hour) meet in a 12-hour period. Somewhat the same concept, but in the opposite direction.
C.J. Smith
2023-11-29 08:29:23 +0000 UTCI found the correct answer with my own proof! If you approximate the 2 circles with regular polygons, whose side lengths are equal but (apothem of the larger shape) = 3*(apothem of the smaller shape), then you’ll find that each time you rotate the smaller polygon from one side onto an adjacent side, it rotates by (360°/n) + E where n is the # of sides of the smaller shape, and E is one of the larger shape’s external angles. When we sum the above expression over all N sides of the larger shape, the left term simply becomes (360N/n)°, and the right term simply becomes 360° (the sum of all external angles of a polygon is 360°, using interior angle theorem). If n is sufficiently large, then N ~= 3n, so the total angle that the small shape turns through is approximately (360° * 3) + 360° = 4*360° = 4 revolutions (the approximation approaches exactness as the polygons approach true circles.) --- I couldn’t find the core idea of this proof anywhere else, so I thought it’d be neat to share.
Andrew Alvarez
2023-11-29 06:44:55 +0000 UTCI really liked it, including the pivot to the solar and sidereal year. And yes, I was totally confused when there was no option to select 4 as an answer.
Robert Blum
2023-11-29 04:12:30 +0000 UTCAfter the coin example and the correct answer of four to the original question, I thought about an inner circle with a radius of zero, so basically a point, for which it is totally intuitive that the answer is one. This single rotation never gets lost, independent of the shape of the inner body. I think this is also nicely illustrated with the triangle example later in the video.
Philipp Wenzelburger
2023-11-28 20:22:15 +0000 UTCFANTASTIC VIDEO! Thoroughly loved it.
Ryan Hamilton
2023-11-28 20:18:52 +0000 UTCIt follows from the paradox! From the perspective of circle A, it only sees itself rotate around circle B 3 times, as shown in the video. But as external observers, we see circle A rotating an extra time (so 4 times total) around circle B. Similarly, we are on Earth so we see from Earth's perspective as it goes around the Sun, and count 365 rotations. But an external observer outside the Solar System would again see an extra rotation - counting 366 rotations. - Emily
Veritasium
2023-11-28 18:41:31 +0000 UTCDone, thanks for pointing that out! - Emily
Veritasium
2023-11-28 18:34:52 +0000 UTCI was disappointed with myself. I picked B(3) using the same straight line circumference intuition, but completely forgot about Sidereal Time which I learned about in my Astrophysics degree 45 years ago.
Allan Peak
2023-11-28 13:45:08 +0000 UTCA great video! It gave me a gut-level appreciation of sidereal time, where before I only understood it as a theoretical concept. However, I have an issue with the whiteboard section with Doug Jungreis - he introduces velocity into the equation, which is very confusing as (to a layman) velocity isn't part of the original problem at all. Would the whole video be much tighter and clearer if that section were cut out?
Mike Milne
2023-11-28 11:22:33 +0000 UTC"Just set up your goals and Brilliant will design a path for you" - that's exactly why I hate this service. I don't want to be spoonfed the knowledge. I want to have a nice catalogue from which I can pull the knowledge based on my current need, mood etc. Yes I tried it.
Bartosz Błaszkiewicz
2023-11-28 11:16:55 +0000 UTCThe wording of the SAT question is pretty poor as I think was pointed out. My biggest problem was with "...will the center of circle first reach the starting point?" Which should of course have an article and thus become: "...will the center of the circle first reach the starting point?"
Gregor Shapiro
2023-11-28 07:08:09 +0000 UTCTo be precise the number of days in a tropical year is approximately 365.242189 and in a sidereal year approximately 365.256363 Perhaps "...more precisely..." as the amount you state is still not precise and the value changes from year to year due to storms and geophysical activity.
Gregor Shapiro
2023-11-28 06:49:24 +0000 UTCAt 6:25, it sounds like you say "Similarily" instead of "Similarly." At 11:39 you say "365.24 to be precise." I would say "365.24 to be more precise." Ancient mathematicians were convinced that all numbers were rational, which slowed the discovery of irrational numbers and the math and science based on them. (We now know there are infinitely more irrational than rational numbers!) In this video, you need not go into how the "approximately 0.24" extra day each year leads to leap years, skipped leap years, and skipped skipped leap years, or how the variation in revolutions also leads to leap seconds. However, the irrationality and the irregularity of the year means you should not say "365.24 to be precise." (You could do a whole video on the subtleties of why not, including centuries of delay in an accurate calendar culminating in the eleven days deleted from 1752.) I was a high school sophomore when this "scandal" occurred, and remember clearly a friend showing me this question that year, so this video was particularly fun for me, and I learned a few new things as always. Thanks for another great video!
Joseph Gill
2023-11-28 04:51:32 +0000 UTCYou got me thinking and my intuitive answer was 3. But it was the phrase in the question about how many times until the center returns that made me pause and do it again using the radius of 4, from center to center of each circle. Very clever! The best part was your explanations using perspective of each object. That was delightful and really made it all make sense. It both rotates AND revolves as it goes around to an outside observer. Great vid, Thank You!
Mr. Hunter Jones
2023-11-28 01:07:27 +0000 UTCI love it. The central point in the explanation, namely that the touching point has a speed of "-V", is merely mentioned. Maybe more emphasis should have been put on that. One editing thing I noticed: There is some pretty bad asynchronicity between Derek's lip movements and his speach sound in parts of the video.
Lionel Pöffel
2023-11-28 01:01:37 +0000 UTCI think I get it now. we are not at the center of the earth so our frame of reference is from the circumference?
katgod
2023-11-28 00:55:11 +0000 UTCThis was very interesting to me as it seems almost magical. although I watched it carefully I am still not certain I understand how the frame of reference makes the number of days change. I will think about it and watch again, I am old which is also a good excuse for not understanding.
katgod
2023-11-28 00:49:43 +0000 UTCI'll also add that the extra black smudge/dot(?) on the actual question is a bit confusing, kind of seems like it is a part of the problem itself. Could be edited out?
StealthSecrecy
2023-11-27 23:59:36 +0000 UTCOne issue I see with bad exam questions like that is someone who understands that the answer might not be 3 would take extra time to think the problem though, possibly further confused when their "right" answer doesn't show up on the multiple choice. Part of being a good test taker is to know when to move on, but I would be a bit upset if I wasted time on a bad question instead of getting more time to work on others.
StealthSecrecy
2023-11-27 23:57:18 +0000 UTCVideo is great !Well - although an engineer - I still am a bit confused... ;-((
Boris Petrovchich
2023-11-27 23:49:07 +0000 UTCAm I having dejavu or is this a repost?
Joeyzoom
2023-11-27 23:17:15 +0000 UTCThis was fascinating—as always!
Adam Foreman
2023-11-27 23:01:49 +0000 UTC
