Here's a trick: Using 1,3,9,27... you can let your audience pick any number of cards _and_ decide if they would like to add or subtract between each component. They tell you their "arbitrary" result, and you can name their cards!
Hah, I knew it that the next thing to try would be the Lucas numbers and then other Fibonacci-like sequences! It does not work with the Padovan nor the Perrin numbers though. Or the Pell, Jacobsthal and other sequence calculated by recurrence relations that I checked.
Thanks. He says that Fibonacci numbers have an extra special property who makes them unique, but the numbers 1,2,4,8,16,... has the same property, and even better, because you can use adjacent numbers of this series.
Every number is uniquely expressible using powers of two, given that you don't use one twice. Isn't this just as 'special' as the Fibonacci numbers in this context? And you don't have to restrict against adjacent powers of two.
Powers of two are very special, that's partially why all of modern technology is built on binary. However that property of powers of two is somewhat more obvious than this property of Fibonacci numbers, which is probably why this property seems more special.
Prof. Mulcahy seemed to suggest that the Fibonacci numbers form a basis analogous to the prime numbers but for addition, saying "that's not true for the other sets of numbers I showed you". I think that's too strong a claim, and the powers of two make a better basis for addition.
I can't be sure what he actually meant but I saw it as a comparison to better explain the nature of this property of the Fibonacci numbers, as a comparison to the primes in this respect. Of course the primes are far more important because they are defined based on this unique decomposition under multiplication, which doesn't actually exist for addition. I think a better description for powers of two would not be a basis for addition but as a basis for counting or a basis for representation, as trying to say its a complete analogue to the primes would suggest that powers of two can't be written as the sum of two numbers (other than zero and itself), just like primes can't be written as the product of two numbers (other than one and itself). In short, I think the property is just as arbitrary for powers of two as it is for Fibonacci numbers, even if there are less restrictions for powers of two.
I thought of using primes and multiplication as an alternative to fibs. So you use 2 3 5 7 J K as your cards, and then ask the audience to multiply the results.
The description says 'more cards and suffering videos' - I suspect that should be 'shuffling'!? XD
mathemagics is awesome
Here's a trick: Using 1,3,9,27... you can let your audience pick any number of cards _and_ decide if they would like to add or subtract between each component. They tell you their "arbitrary" result, and you can name their cards!
How many fibs could a little fib fib if a little fib could fib fibs?
e^(iπ) non factorial exclamation point _!_
euler didn't like the power that imaginary pie had, so no!
+and then i said the factorial would not make any effect
thank you very much for the video !
i liked the info on fibonacci numbers
mathemagical things are cool xP
Hah, I knew it that the next thing to try would be the Lucas numbers and then other Fibonacci-like sequences! It does not work with the Padovan nor the Perrin numbers though. Or the Pell, Jacobsthal and other sequence calculated by recurrence relations that I checked.
If I may ask, about the decomposing of a number by Fibonacci numbers in a unique way. I didn't understand the 2nd rule. Can anyone explain it to me?
Thanks.
He says that Fibonacci numbers have an extra special property who makes them unique, but the numbers 1,2,4,8,16,... has the same property, and even better, because you can use adjacent numbers of this series.
Every number is uniquely expressible using powers of two, given that you don't use one twice. Isn't this just as 'special' as the Fibonacci numbers in this context? And you don't have to restrict against adjacent powers of two.
Powers of two are very special, that's partially why all of modern technology is built on binary. However that property of powers of two is somewhat more obvious than this property of Fibonacci numbers, which is probably why this property seems more special.
Prof. Mulcahy seemed to suggest that the Fibonacci numbers form a basis analogous to the prime numbers but for addition, saying "that's not true for the other sets of numbers I showed you". I think that's too strong a claim, and the powers of two make a better basis for addition.
I can't be sure what he actually meant but I saw it as a comparison to better explain the nature of this property of the Fibonacci numbers, as a comparison to the primes in this respect. Of course the primes are far more important because they are defined based on this unique decomposition under multiplication, which doesn't actually exist for addition. I think a better description for powers of two would not be a basis for addition but as a basis for counting or a basis for representation, as trying to say its a complete analogue to the primes would suggest that powers of two can't be written as the sum of two numbers (other than zero and itself), just like primes can't be written as the product of two numbers (other than one and itself). In short, I think the property is just as arbitrary for powers of two as it is for Fibonacci numbers, even if there are less restrictions for powers of two.
The point is you can't do it with the Lucas numbers I think.
I thought of using primes and multiplication as an alternative to fibs.
So you use 2 3 5 7 J K as your cards, and then ask the audience to multiply the results.
Could use ace too
Henrix98 1 isn't a prime, so no
+Nikolaj Lepka Doesn't matter, the trick would work with one more card
Henrix98 it would, but then it wouldn't be primes anymore
Yeah but primes are also well known, like powers of 2
4th
500 views and 5th comment.
869 likes to 1 dislike. Never seen anything like that!