Can you solve the Alice in Wonderland riddle? - Alex Gendler
-
0:08 - 0:10After many adventures in Wonderland,
-
0:10 - 0:13Alice has once again found
herself in the court -
0:13 - 0:15of the temperamental
Queen of Hearts. -
0:15 - 0:18She’s about to pass through the garden
undetected, -
0:18 - 0:22when she overhears the king
and queen arguing. -
0:22 - 0:28“It’s quite simple,” says the queen.
“64 is the same as 65, and that’s that.” -
0:28 - 0:32Without thinking, Alice interjects.
“Nonsense,” she says. -
0:32 - 0:39“If 64 were the same as 65,
then it would be 65 and not 64 at all.” -
0:39 - 0:41“What? How dare you!” the queen huffs.
-
0:41 - 0:44“I’ll prove it right now,
and then it’s off with your head!” -
0:44 - 0:46Before she can protest,
-
0:46 - 0:51Alice is dragged toward a field
with two chessboard patterns— -
0:51 - 0:55an 8 by 8 square and a 5 by 13 rectangle.
-
0:55 - 1:00As the queen claps her hands,
four odd-looking soldiers approach -
1:00 - 1:04and lie down next to each other,
covering the first chessboard. -
1:04 - 1:12Alice sees that two of them are trapezoids
with non-diagonal sides measuring 5x5x3, -
1:12 - 1:19while the other two are long triangles
with non-diagonal sides measuring 8x3. -
1:19 - 1:21“See, this is 64.”
-
1:21 - 1:23The queen claps her hands again.
-
1:23 - 1:26The card soldiers get up,
rearrange themselves, -
1:26 - 1:29and lie down atop the second chessboard.
-
1:29 - 1:32“And that is 65."
-
1:32 - 1:36Alice gasps. She’s certain the soldiers
didn’t change size or shape -
1:36 - 1:38moving from one board to the other.
-
1:38 - 1:43But it’s a mathematical certainty
that the queen must be cheating somehow. -
1:43 - 1:47Can Alice wrap her head around what’s
wrong— before she loses it? -
1:47 - 1:50Pause the video to figure it out yourself.
Answer in 3. -
1:50 - 1:52Answer in 2
-
1:52 - 1:54Answer in 1
-
1:54 - 1:59Just as things aren’t looking too good
for Alice, she remembers her geometry, -
1:59 - 2:03and looks again at the trapezoid
and triangle soldier -
2:03 - 2:05lying next to each other.
-
2:05 - 2:08They look like they cover exactly half
of the rectangle, -
2:08 - 2:13their edges forming one long line
running from corner to corner. -
2:13 - 2:16If that’s true, then the slopes
of their diagonal sides -
2:16 - 2:17should be the same.
-
2:17 - 2:20But when she calculates these slopes
-
2:20 - 2:23using the tried and true formula
"rise over run," -
2:23 - 2:26a most curious thing happens.
-
2:26 - 2:31The trapezoid soldier’s diagonal side
goes up 2 and over 5, -
2:31 - 2:35giving it a slope of two fifths, or 0.4.
-
2:35 - 2:40The triangle soldier’s diagonal, however,
goes up 3 and over 8, -
2:40 - 2:45making its slope three eights, or 0.375.
-
2:45 - 2:47They’re not the same at all!
-
2:47 - 2:50Before the queen’s guards can stop her,
-
2:50 - 2:54Alice drinks a bit of her shrinking potion
to go in for a closer look. -
2:54 - 2:59Sure enough, there’s a miniscule gap
between the triangles and trapezoids, -
2:59 - 3:03forming a parallelogram that stretches
the entire length of the board -
3:03 - 3:06and accounts for the missing square.
-
3:06 - 3:10There’s something even more curious
about these numbers: -
3:10 - 3:13they’re all part of the Fibonacci series,
-
3:13 - 3:17where each number is the sum
of the two preceding ones. -
3:17 - 3:21Fibonacci numbers have two properties
that factor in here: -
3:21 - 3:25first, squaring a Fibonacci number
gives you a value -
3:25 - 3:27that’s one more or one less
-
3:27 - 3:31than the product of the Fibonacci numbers
on either side of it. -
3:31 - 3:36In other words, 8 squared is one less
than 5 times 13, -
3:36 - 3:40while 5 squared is one more
than 3 times 8. -
3:40 - 3:46And second, the ratio between successive
Fibonacci numbers is quite similar. -
3:46 - 3:52So similar, in fact, that it eventually
converges on the golden ratio. -
3:52 - 3:56That’s what allows devious royals
to construct slopes -
3:56 - 3:58that look deceptively similar.
-
3:58 - 4:03In fact, the Queen of Hearts could cobble
together an analogous conundrum -
4:03 - 4:06out of any four consecutive
Fibonacci numbers. -
4:06 - 4:11The higher they go, the more it seems
like the impossible is true. -
4:11 - 4:15But in the words of Lewis Carroll—
author of Alice in Wonderland -
4:15 - 4:19and an accomplished mathematician
who studied this very puzzle— -
4:19 - 4:22one can’t believe impossible things.
- Title:
- Can you solve the Alice in Wonderland riddle? - Alex Gendler
- Speaker:
- Alex Gendler
- Description:
-
View full lesson: https://ed.ted.com/lessons/can-you-solve-the-alice-in-wonderland-riddle-alex-gendler
After many adventures in Wonderland, Alice has once again found herself in the court of the temperamental Queen of Hearts. She’s about to pass through the garden undetected, when she overhears the king and queen arguing that 64 is the same as 65. Can Alice prove the queen wrong and escape unscathed? Alex Gendler shows how.
Lesson by Alex Gendler, directed by Artrake Studio.
- Video Language:
- English
- Team:
- closed TED
- Project:
- TED-Ed
- Duration:
- 04:24
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Tara Ahmadinejad edited English subtitles for Can you solve the Alice in Wonderland riddle? | ||
Tara Ahmadinejad edited English subtitles for Can you solve the Alice in Wonderland riddle? | ||
Tara Ahmadinejad edited English subtitles for Can you solve the Alice in Wonderland riddle? | ||
Tara Ahmadinejad edited English subtitles for Can you solve the Alice in Wonderland riddle? |