A little trick to sum Fibonacci numbers. Try it out.
Пікірлер: 520
@nychold8 жыл бұрын
Why it works: a b a + b a + 2b 2a + 3b 3a + 5b 5a + 8b 8a + 13b 13a + 21b 21a + 34b ---------------- 55a + 88b = 11(5a + 8b) ...which is 11 times the 4th number from the bottom.
@belowaverageplayer7178 жыл бұрын
You're the real MVP. I was left empty after the video.
@ArloLipof8 жыл бұрын
@Spencer 3035 No, he isn't. He just copied my comment from the day before...
@nychold8 жыл бұрын
LDHFIntegrale Actually, I worked it out myself. But nice conceit there.
@ArloLipof8 жыл бұрын
And a liar at that. Sad.
@nychold8 жыл бұрын
LDHFIntegrale Cool story bro. Too bad it's fiction.
@SirSethery8 жыл бұрын
Except I don't know anyone who wouldn't screw up the adding part.
@ipassedtheturingtest13968 жыл бұрын
same
@jfb-8 жыл бұрын
Give them a calculator
@sirjohnnyg8 жыл бұрын
a = first number (F1) b = second number (F2) F3 = a + b F4 = a + 2b ... F7 = 5a + 8b ... Sum F1 through F10 = 55a + 88b F7*11 = F10 Symmetric if you write them in the other order to start.
@thegrandmuftiofwakanda8 жыл бұрын
I don't have any friends that can add 2 numbers together, sorry.
@nonrompereddddffd54508 жыл бұрын
i dont have friends at all
@aifesolenopsisgomez6057 жыл бұрын
Non Rompere Ddddffd :'( me neither
@thegrandmuftiofwakanda7 жыл бұрын
Lolzords. I wasn't saying I don't have friends. I do. They are just morons.
@nanigopalsaha24084 жыл бұрын
@@thegrandmuftiofwakanda They probably think a moron is a particle.
@GiladTeller8 жыл бұрын
My friend told me a Fibonacci joke, it was as bad as the last two combined.
@gojoubabee8 жыл бұрын
Haha nice. I also have a joke, this one's about Fermat; but the problem is I don't think it will fit in the comment section.
@whitherwhence8 жыл бұрын
+MegaMrFroggy l have found a truely marvellous joke about Fremat, this comment section is to narrow to contain.
@SpiffyCheese27 жыл бұрын
Don't Steal Arthur Benjamin's joke!
@CameronChardukian5 жыл бұрын
I saw this on another video, but I just now understand lol
@qbwkp8 жыл бұрын
I did this in school, I now have 3 girlfriends and 7 side-chicks. All of them products of my vast intellect of course.
@BigDBrian8 жыл бұрын
so they're imaginary? do you even go to school? what is real anymore!??
@julianjimenez40468 жыл бұрын
+mrBorkD Is this the real life? Is this just fantasy?
@someguyusingyt90918 жыл бұрын
Causing a landslide No escape from reality Face the truth
@ubererhs28988 жыл бұрын
open your eyes
@ubererhs28988 жыл бұрын
+Mendel Chow caught in a landslide*
@mattyfox6668 жыл бұрын
I tried this at my friends house, they called me a nerd and beat the piss out of me, thanks a bunch
@singingbanana8 жыл бұрын
+mattyfox666 You need better friends
@jimmythewig33545 жыл бұрын
@@singingbanana I don't think he was being serious... :)
@orangeshoes4 жыл бұрын
@@jimmythewig3354 I don't think he was being serious either... :P
@rith3593 жыл бұрын
@@singingbanana Can we be friends?
@lilliangrace95053 жыл бұрын
I used to add the fibonacci numbers to get to sleep. numbers and patterns have always brought me peace. Thank you for this trick! It's fun and great knowledge
@evanfortunato23824 жыл бұрын
this man really just hit us with "the proof is left as an exercise to the reader"
@Doeniz15 жыл бұрын
I played around with this a little bit and observed the following: To every second number (all on odd positions) there is a point, where all numbers summed together are a multiple of this particulary number: The sum of the first three numbers is always two times the third. The sum of the first six numers is always four times the fifth. The sum of the first ten numbers is always eleven times the seventh. (The subject of the video) The sum of the first fourteen numbers is always 29 times the ninth. The sum of the first eightteen numbers is always 76 times the eleventh. The sum of the first 22 numbers is always 199 times the thirteenth. It feels like the sum of the first 4n-2 numbers is always k times the (2n+1)th number, but I can't find a pattern in the k values. I would be glad if James could make another video about this where he explains the patterns
@TheSucread8 жыл бұрын
Well this induction proof is astoundingly simple. You don't even need a piece of paper. Just pause a video and do it in your head. Beautiful piece of mathematics James!
@singingbanana8 жыл бұрын
It is - I was considering doing it for the video, but decided people who know induction can do it themselves, and people who don't will just enjoy the bit with the trick.
@jasonwilson15818 жыл бұрын
Thank you, Dr. Grime! I'll show this to the middle school students in my Intro to Number Theory class today.
@singingbanana8 жыл бұрын
Perfect. I thought this would be one for teachers :)
@jasonwilson15818 жыл бұрын
The kids loved it. I did it a few times with the class & they copied down the examples. After two days, most of the kids, either through trial & error or algebra, found the pattern. A couple of them are now seeing how far they can take it out to find an easy multiplication trick for a longer series of numbers.
@MG300018 жыл бұрын
multiplying by 11 much easier: n * 10 + n
@heyitsalex998 жыл бұрын
i agree lol
@ehsan_kia8 жыл бұрын
That's basically the same thing. Times 10 you just add a zero, but then the addition is the slightly slower part, but if you think about it, that's basically exactly what his trick is doing. You can ignore the first digit since it's being added to 0 and won't carry over, so you only care about the middle digit carrying.
@ricato28 жыл бұрын
That's the normal way. His way is much faster
@Shadowmere298 жыл бұрын
This way is the exact same as what is shown in the video. There are no fewer and no extra steps.
@Cream147player7 жыл бұрын
You will never get as quick doing it that way as his way. T'is the difference between adding a 3 digit number and a 2 digit number, and adding two 1 digit numbers. It's obvious which is actually easier.
@benbradley_1238 жыл бұрын
I'm going to this year's Fibonacci Convention - apparently, it's going to be as big as the last 2 put together!
@weckar8 жыл бұрын
I realize it's a little off-topic, but it needs to be said that you have the most contagious smile on the internet.
@azyfloof8 жыл бұрын
That's smart :D Beats the crap out of those "subtract the number you first thought of, your answer's 9" type 'tricks' :P
@denummer18936 жыл бұрын
That is Sooooo true
@PrinceKumar-nu6ik6 жыл бұрын
1to 20 countine chosse any 6 number sum is 20 wo konsa number hoge jin 6 number ka sum 20 hoga
@RedTiGeRJJ8 жыл бұрын
Thank you ! I will try this tomorrow with my teacher!
@singingbanana8 жыл бұрын
Yes! :D
@kasperm.r.guldberg73548 жыл бұрын
Great stuff, James! The multiply-by-11-trick reminded me of old Trachtenberg! His ghost lives on... Keep the videos coming when you've time.
@SPACKlick8 жыл бұрын
Paused at 2:05 to wok out the answer. Each term is as follows (x,y,x+y,x+2y,2x+3y,3x+5y,5x+8y,8x+13y,13x+21y,21x+34y) which sums to 55x+88y, the fourth term from the bottom is 5x+8y which is 1/11 of the sum. I'm sure there are other things you can do with this because the coefficients are all fibonacci numbers. e.g. Sum to the 6th term is 4 times the 5th term. and sum to 14th is 29 times the 9th term
@guitarinos8 жыл бұрын
well done, but what do you mean by other things that can be done with this?
@SPACKlick8 жыл бұрын
As shown in the e.g. I'm sure there are other sets of numbers you could use to get something with this.
@chrisg30308 жыл бұрын
In your e.g. you note that sum to the 6th term is 4 times the 5th term, and sum to the 14th is 29 times the 9th term. We can also see that sum to the 18th is 76 times the 11th term, sum to the 22nd is 199 times the 13th term and so on. What I find fascinating is that while the coefficients in your nx + my expressions are Fibonacci numbers, 4, 11 (James' example), 29, 76, and 199 are alternate Lucas numbers. And the next alternate Lucas term down from 4, namely 1, can be derived from "sum to the 2nd term is 1 times the 3rd term".
@eacy7deacy8 жыл бұрын
Let's choose the numbers x and y 1. x 2. y 3. x+y 4. x+2y 5. 2x+3y 6. 3x+5y 7. 5x+8y 8. 8x+13y 9. 13x+21y 10. 21x+34 The sum of all these is 55x+88y=11*(5x+8y) which is the 7th column.
@Luffy_wastaken4 жыл бұрын
Or the last 4th...
@yonigolombek33353 жыл бұрын
@@Luffy_wastaken and extend it for the other fact: 11. 34x+55y 12. 55x+89y 55x+88y=55x+89y-y
@WhiteRAZOR8 жыл бұрын
In 1995 when I was in grade 2 I looked like a genius when I could multiply by 11. I tried showing this off to a few friends just then and they just said something along the lines of "can't math. Art degree". I miss primary school. I had morale.
@sk8rdman8 жыл бұрын
When I was in highschool I developed a system for quickly squaring 2 digit numbers in my head. It was great for my physics and algebra homework, but nobody else really cared "cuz calculators".
@WhiteRAZOR8 жыл бұрын
Ah the tech generation problem. I mean, I don't think it's a problem like our older generation says, but it's always interesting and admirable to hear about self discoveries. In school I also self-discovered how to add two fractions with unlike denominators. We were learning about LCM at the time using the tedious 'list all factors' method. I discovered that I could just multiply each fraction with the other denominator to produce like fractions. It didn't produce the lowest multiple denominator but I solved my exercises in a less tedious and more efficient way. This got me some grief for not doing the task at hand actually. I didn't know what I was doing at the time but I discovered it worked for all fractions. My mind was blown. Only when we learnt algebra (in the following year?) I proved to myself a/b + c/d = ad/bd + cb/db. Mind blown again!
@azlhiacneg8 жыл бұрын
I'm so showing this to my discrete math professor. Fibonacci and induction. I don't know what could get him more excited. :D
@DitDede8 жыл бұрын
thanks! my 10 yo son loved it - and ended up learning how to multiply by 11. He was even able to prove it: 55a+88b = 11(5a+8b)
@singingbanana8 жыл бұрын
+DitDede This has made my day!
@boumbh8 жыл бұрын
Generalization for any: f a Fibonacci series n a natural number k an odd natural number L the Lucas series (2, 1, 3, 4, 7, 11, 18...) f(n+2k) = L(k+1) × f(n+k) + f(n) For n = 2, you get f(2+2k) = L(k+1) × f(n+k) + f(2) f(2k+2) − f(2) = L(k+1) × f(2+k) Sum of all the elements of f from 1 to 2k = L(k+1) × f(2+k) Example for n = 2, k = 5 : f(2+2×10) = L(5+1) × f(2+5) + f(2) f(12) = L(6) × f(7) + f(2) f(12) − f(2) = 11 × f(7)
@chrisg30308 жыл бұрын
The connection between this trick and the Lucas sequence can also be expressed as follows: When your volunteer V gets to the seventh number (S7) in her/his sequence, then you multiply that number by 11 to get the partial sum for S10, as Dr Grime showed. When V gets to S9, you multiply by 29 to get the partial sum for S14. When V gets to S11, you multiply by 76 and get the ps for even further ahead, namely S18. And so on. These multipliers are alternate terms in the Lucas sequence, and if you can memorise them (or just use it openly as a reference) you can still come up with results to impress your friends even though you probably have to use a calculator. You can go in the opposite direction down from S7 too of course: at S5 the multiplier is 4 to get the ps for S6. And at S3 you multiply by 1 to retrodict rather than predict the ps for S2.
@Aerialyn6 жыл бұрын
I'm lucas
@martinepstein98265 жыл бұрын
Instead of using induction I rewrote it as a telescoping sum. F(1) + F(2) + ... + F(n-1) + F(n) = (F(3) - F(2)) + (F(4) - F(3)) + ... + (F(n+1) - F(n)) + (F(n+2) - F(n+1)) = -F(2) + F(n+2)
@Dank_SomeOne7 жыл бұрын
its crazy how every fibbonacci sequence is unique
@Maninawig7 жыл бұрын
I love this trick! I am also interested in mathematical tricks such as 1089, which takes a random number, does a few calculations that don't cancel themselves out (like Add 3, multiply by 2, subtract 6, now divide it in half), but I am having a hard time to search out more of these equations. Do you know if these types of equations have a group name or something to help my search?
@NFSHeld2 жыл бұрын
What you described cancels itself out... x (add 3) x+3 (multiply by 2) 2x+6 (subtract 6) 2x (divide in half) x. 😁
@teuthida16578 жыл бұрын
Proving the sum formula by linear algebra is a good exercise too. It isn't as straightforward as induction, but it lets you find out the thesis by yourself.
@fablungo8 жыл бұрын
Or have a race to the 12th number, let them do all the hard work and when they get to the 6th number, multiply by 11, add the second one and write that down. Probably more impressive with big numbers, but it will seem like you were doing in your head faster than they could do it with paper.
@mrrubixcubeman8 жыл бұрын
I have a question. What do you do for a living? Are you a teacher? How do you make your money? This would be like the best life ever for me. Your videos are great!
@Minecraftster1487908 жыл бұрын
I think he might be a professor at Cambridge. Not sure though
@VicvicW8 жыл бұрын
I thought it was Nottingham.
@heyitsalex998 жыл бұрын
proffessor at nottingham
@tj127118 жыл бұрын
+tman301j He taught courses on Cryptography at Cambridge Link: www.ice.cam.ac.uk/components/tutors/?view=tutor&id=1892&cid=6842
@pegy63848 жыл бұрын
He used to work with the Millennium Maths Project at Cambridge, but he is a freelance maths presenter now. He has several different presentations that he gives in the UK and around the world, but the topic he's probably best known for is the cryptography of the Enigma machine. He has addressed it in various videos and on his website.
@SchuldinerLA8 жыл бұрын
Good trick! The proof is fairly easy once you prove (with induction, as you said) that thing about the sum of Fibonacci numbers. Thank you very much for the videos you make here and with numberphile!
@thomasalexander15637 жыл бұрын
Can't wait to see more in this channel and numberphile.. Thank you
@brunosouza86407 жыл бұрын
I love you man, you are amazing! Your vids on numberphile are my favourite as well! The excitement on your eyes everytime you share new facts and curtiosities really brings out my curiosity for math! (Even though i hate algebra!) Shout outs from Brazil!
@bryphi778 жыл бұрын
This trick just got me layed!
@RealCadde8 жыл бұрын
Your spelling suggests you are in kindergarten. That's dirty.
@bryphi778 жыл бұрын
Cadde Cant you go torture someone on a grammar channel?
@RealCadde8 жыл бұрын
bryphi77 Can't you go learn how to spell? Or go play in your sandpit kid.
@bryphi778 жыл бұрын
+Cadde So you have never made a typo? That is impressive! You are definitely the intellectual superior of us. Sleep well tonight knowing that you have corrected a grammer error of a lesser human.
@gojoubabee8 жыл бұрын
*grammar
@MrMas97 жыл бұрын
Was really awesome seeing you today at the Institution of Education man! Thoroughly enjoyed the talk :)
@ironman-br8hw7 жыл бұрын
Wanna hear a good fib? Dancer says blitzen speaks elven; blitzen says yes; dancer says blitzen speaks 'other' languages as well; blitzen says yes; Dancer wants to know if blitzen is lying.
@TheDonuts428 жыл бұрын
An easier way to do the n case is to double the last number, then add the second to last number, then subtract the second number.
@BigDBrian8 жыл бұрын
Lemme check, does 2f(n)+f(n-1)-f(2) equal f(n)+f(n+1)-f(2)? 2f(n)+f(n-1)=f(n)+f(n+1) f(n)+f(n-1)=f(n+1) correct(because of the definition of fibonacci numbers, woo!)
@ekroz28908 жыл бұрын
Liked the math, loved the little mouse in the corner of the chalkboard.
@ferncat13978 жыл бұрын
I love watching your videos. They always leave a smile on my face. Your passion and enthusiasm are infectious! Thank you!
@aradhyeagarwal18358 жыл бұрын
This is really easy James; you write the first number as a and the second number as d and the write all the ten numbers in terms of a and d and then calculate their sum in terms of the same, and one would find that it is 11 times the 4th number from the bottom.
@KRYPTOS_K54 жыл бұрын
Excellent lesson. Shorter, clearer, funnier and more complete than the average competitors. It would be interesting to show the "minus second term" pattern during the sums using a table in order to show the inductive pattern explicitly.
@cQunc6 жыл бұрын
Instead of doing a couple more steps, you can stick with what you have. F(n+2) = F(n+1) + F(n) = (F(n) + F(n-1)) + F(n) = 2F(n) + F(n-1). So you're calculating 2F(n) + F(n-1) - F(2).
@johnroberts71858 жыл бұрын
You're always excited when you're talking about maths. It's a shame that more people aren't like that.
@benjammin81848 жыл бұрын
Do you ever get tired of being such a maths legend?
@fergusmaclachlan14047 жыл бұрын
Who would get tired of being a maths legend?
@iyoutome6 жыл бұрын
Thanks brother, starting over again is absolutely awesome. Good thing I'm retired....lol p.s., teaching this to my 6yr old Niece.
@hydorah8 жыл бұрын
Your easy multiply by 11 method is a bit mental! Very creative! I just multiply by ten and add the quantity multiplied to that once, to make 11 x whatever. But seeing yours was intriguing. Alround good vid
@andrewlouie28 жыл бұрын
My friends are going to think I'm so cool!
@sSunbeamM8 жыл бұрын
you are probably the worlds most demonstrative example of "how it is like to be in a passion" (?)
@michaelempeigne35197 жыл бұрын
nth term formula for the fibonacci sequence derivation 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, .............. F_n = F_(n - 1 ) + F_(n - 2 ) I like to call the first term as the 0th term. Let F_n = r^n so F_(n - 1 ) = r^( n - 1 ) and F_(n - 2 ) = r^( n - 2 ) That means that r^n = r^( n - 1 ) + r^( n - 2 ) 1 = ( 1 / r ) + ( 1 / r^2 ) r^2 = r + 1 r^2 - r - 1 = 0 using the quadratic formula we obtain : r_1 = ( 1 + sqrt ( 5 ) ) / 2 and r_2 = ( 1 - sqrt ( 5 ) ) / 2 Now let F_n = a*( r_1 )^n + b*(r_2 )^n F_n = a * [ (1 + sqrt 5 ) / 2 ]^n + b * [ ( 1 - sqrt 5 ) / 2]^n Let's try it for the first two terms since it is going to be the easiest values. 1 = a + b 1 = a * [ ( 1 + sqrt 5 ) / 2 ] + b * [ ( 1 - sqrt 5 ) / 2 ] solving the system of two equations yields : b = ( - 1 / sqrt 5) [ ( 1 - sqrt 5 ) / 2] a = ( 1 / sqrt 5 ) * [ (1 + sqrt 5 ) / 2 ] Now to back substitute : F_n = ( 1 / sqrt 5 ) * [ ( 1 + sqrt 5 ) / 2 ]^( n + 1 ) - ( 1 / sqrt 5 )* [ ( 1 - sqrt 5 ) / 2 ]^( n + 1 )
@xukaili82727 жыл бұрын
And then the revived John Von Neumann solves the same sequence before you can times 11 in your head.
@DjVortex-w8 жыл бұрын
There's one small problem with this trick. If they make any mistake while creating that list, your answer will be incorrect, and when they check it eg. with a calculator, and your answer does not match, it becomes clear that you tried to use trickery. In order to make sure that your trick works, you would need to check that they calculated all the numbers correctly.
@U014B8 жыл бұрын
Aww, there's a little mouse in the bottom corner of your chalkboard! Also, what do magnets have to do with proving the F(n+2)-F(2) thing?
@DeltaForce15228 жыл бұрын
Can't tell if that question is a joke, but I'll answer anyways. He isn't referring to electromagnetic induction, but mathematical induction. It's a proof technique, if you want to look it up.
@akosslemmer46038 жыл бұрын
I was thinking the same, with the induction....
@kongstrong19385 жыл бұрын
My friends can't add. I show them a mirror and they think I am an alien.
@RasKamun18 жыл бұрын
I did this a a magic trick. Finally won me a beer, by betting my friend, my math teacher wouldn't know F7 * 11 = E (1-10) Fi
@varunnrao32767 жыл бұрын
Hey Amazing vid !! I am just curious about your opinion on Vedic Mathematics
@gtziavelis8 жыл бұрын
James, try starting out with 133/11 or 12+1/11 for both the numbers, for a nice little surprise
@rebia55427 жыл бұрын
do you know the 111 trick? it just a cool little design under the number. For Example: 231×111= 25641 - (it's easier to show on paper) --- you write down the last ------ number, 1. Then the last two --- added, 4. Then all three, 6. - Then the first two, 5. And finally, just the 2.
@joaocabral35417 жыл бұрын
I really like how enthusiastic you are when making this video
@MexieMex8 жыл бұрын
I've been using this trick to win beer in proposition bets for years ;^>
@brainbytes12027 жыл бұрын
Thanks for the video! As usual, your videos are awesome!
@leorocha236 жыл бұрын
absolutely LOVE THIS!! :D I wish I had you as my math teacher :D
@theo73718 жыл бұрын
Since many people her like Lucas sequences, I propose a pretty fun problem to examine: Suppose we create a sequence by taking any two real numbers (x and y) and extend the sequence with the Lucas sequence rule (every next term is equal to the sum of the previous two) but also extend it to the other end (with the rule that every previous term is equal to the difference between the next ones. So the general sequence with x and y would have the form: .... -3x+2y, 2x-y, -x+y, x, y, x+y, x+2y, 2x+3y, .... Let's name the terms: .... a(-1)=-x+y, a(0)=x, a(1)=y, .... Show that as n goes to infinity: lim(a(n)/a(n-1))=φ for almost every sequence and that as n goes to minus infinity this limit goes to -1/φ for almost every sequence. The key to my solution to this was finding the small special group of sequences for which this is not true and making a clever observation.
@iwersonsch51317 жыл бұрын
The trick is that, with the Fibonacci numbers, is that the n-th number is just the first number times the (n-2)th Fibonacci number plus the second number times the (n-1)th Fibonacci number. So we're just gonna count: 1-1-2-3-5-8-13-21-34-55 So the 7th number is 8 times the second number plus 5 times the first number, while the sum is (34+21+13+8+5+3+2+1)=88 times the second number and (21+13+8+5+3+2+1+1)=55 times the first number, which is just 11 times the 7th number. Ah, and we also see that the sum of those numbers is (the (n+1)th Fibonacci number -1) times the second number, plus the n-th Fibonacci number times the first number.
@akshhay7 жыл бұрын
Fibonacci numbers were discovered in India centuries before by the art of music
@CastorQuinn8 жыл бұрын
Fn marvelous.
@singingbanana8 жыл бұрын
+Castor Quinn Ha!
@javier89208 жыл бұрын
I FOUND HIM. YES.
@mal2ksc8 жыл бұрын
Multiplying by 11 is as simple as this: First multiply by 10. (Just add a freaking 0 to the end.) Then add the original number to that. Multiplying by 9 is almost as easy, you just _subtract_ the original number as the last step. It works for other 10n±1 cases as well. Multiply by 21? First multiply by 2, and tack on the 0. Then add the original number. Multiply by 39? Multiply by 4, tack on the 0, subtract the original number. No matter the number of digits involved, the rules don't change.
@CardTrickBoysHD8 жыл бұрын
Hi James nice to have you back on the Tube!
@claudiocampanella24293 жыл бұрын
Jack is married looking at Anna that if she is not married the answer is "A" yes. In the event that she is married she is looking at George that is not married and therefore Anna is the married person looking at unmarried George, the answer is a definite "A"
@mahmoudelsharawy54058 жыл бұрын
My friend literally showed me this trick a few days before this came out.
@bretthaupt10194 жыл бұрын
It should be noted that this is not unique to 10 values. There is an equivalent formula thathappens every 4n+2, just with a different constant. For instance, the sum of 30 numbers is 1364 times the 17th number in the sequence.
@bretthaupt10194 жыл бұрын
I should elaborate that the constant will be ϕ (1 + ϕ)^(4n+2) + (1 - ϕ) (2 - ϕ)^(4n+2), where ϕ is the golden ratio.
@williamrutherford5538 жыл бұрын
You weren't lying when you said the proof was easy. That's the only time I think the basis was harder to prove than the induction hypothesis.
@singingbanana8 жыл бұрын
+William Rutherford I agree!
@thalisthes7 жыл бұрын
We are currently doing induction in math, and because our teacher is a non-native speaker he always pronounces "assume" as "asshume" and it always cracks me up :P Great video btw.
@reecegielen92958 жыл бұрын
Someone help me out here - been too long since I've engaged in any kind of mathematics here... Seems to me that each step can be written as pairs of consecutive Fibbonaci numbers, multiplied by your starting numbers a and b , i.e. Term (N) = F(k)*a+F(k+1)*b, and that the sum described can then be termed as Sum(T1-TN) = a(Sum(F1 to F(N-2))+1) + b(Sum(F1 to F(N-1))), where F1 = 1, F2=1, F3=2, F4=3, F5=5 ... How would you frame such a formula in standard notational conventions? Missed out on statistical mathematics during my school days. Also any holes in the thought process, feel free to bring them to my attention, with the appropriate amount of ridicule of course. EDIT: Note that this applies from Step 4 or 5 onwards, forgot to account for the initial conditions. Yes, yes, I know.
@charlottedarroch8 жыл бұрын
A more general version of this trick is to say S(4n+2)=L(2n+1)*F(2n+3), where F(n) is the nth number in your generalised Fibonacci sequence, S(n)=F(1)+F(2)+...+F(n) and L(n) is the nth Lucas number, indexed with L(0)=2, L(1)=1. This video covers the case where n=2, so S(10)=L(5)*F(7), and indeed the 5th Lucas number is 11. The remaining congruences classes mod 4 are not quite as neat, with S(4n)=L(2n+1)*F(2n+1)-F(1), S(4n+1)=L(2n+1)*F(2n+2)+F(1)-F(2) and S(4n+3)=L(2n+1)*F(2n+4)+F(1).
@nunyabiznis35953 жыл бұрын
x*11 = x*10+x which in many cases is waaaaaaay quicker ie 53*10=530+53=583
@AinaweeUAE8 жыл бұрын
I have a question. For the last trick, F(n+2) - F(2) is the sum F(1) + F(2) + ... + F(n). But the order of the first 2 numbers doesn't matter, so doesn't that mean the answer would not be always correct? Like what if the example you gave was 5 + 8 + ..., then F(2) is 8 and the sum you get is 885 - 8 = 878? What am I missing?
@WayneSinclair18 жыл бұрын
But then F(4) would be 13 + 8 instead of 13 + 5 and so it would lead to a whole different sequence of numbers.
@uddhavgoel26568 жыл бұрын
Hey I have seen the same trick on the channel "scam school" by Brian brushwood. Any chance you know him?
@singingbanana8 жыл бұрын
Oh! I had no idea! I do know Brian, we're internet pals. I hope someone will reply with the link.
@OsamaRana8 жыл бұрын
His delivery is a lot more forced. Plus, that hairstyle.
@singingbanana8 жыл бұрын
Thanks. Ah, it was five years ago - I think that's acceptable. Good old Brian.
@Shadowmere298 жыл бұрын
I heard about this trick about 8 years ago when I was 9 from a book called Secrets of Mental Math by Arthur T. Benjamin and Michael Shermer. Have you heard of either of them?
@WalterKingstone8 жыл бұрын
Ishaan Sabnis I have, that's where I first saw this trick too. Arthur Benjamin's amazing.
@heyitsalex998 жыл бұрын
people like you, matt parker, steve mould etc. live the life i really wanna live, but first i must do a maths degree, i hope i get in to the uni ive chosen
@candeevaniderstine80648 жыл бұрын
Love all your videos! Thanks so much.
@UKcuber4 жыл бұрын
If you do 2 numbers between 1 and 10 you could just memorise the answers since there's only 18 or 19 total possibilities depending on if you allow duplicates.
@hansmuller18468 жыл бұрын
Sittin there thinkin "What the f*ck, this actually works"
@astropgn8 жыл бұрын
Yey, I prove it without looking at the comments before. Thanks, singingbanana, you are making me do math!
@chrisg30308 жыл бұрын
Shorter if harder version of the trick: ask your volunteer to write a column of just six numbers using the same method. When s/he gets to the fifth you can multiply it by 4 to get the sum of all six numbers. So in James' first example: 8+5+13+18+31+49 = 124 = 4x31. Here's an even shorter one if you're in a hurry: 8+5+13 = 26 = 2x13. (What about longer versions?)
@MG300018 жыл бұрын
I tried math tricks at a party once. Since then I visited no more parties :/
@Qermaq8 жыл бұрын
If I haven't been watching, can I still get thanks?
@TheEarthCreature8 жыл бұрын
Another way I think of x11s is you add the number to itself plus an extra digit 0 at the end.... for example 11 x 11 = 121 = 11 + 110, or 126163984 x 11 = 126163984 + 1261639840 = 1387903824 It seems to take me roughly about the same amount of time to do it this way as to do it your way, with probably a couple more seconds dedicated to writing the number over before addition.
@Fiyaaaahh8 жыл бұрын
If you had given the multiply-by-11 trick it's own video I would have been perfect fine with that lol. That's a nice trick.
@jamestaylor19348 жыл бұрын
Curiouser and curiouser!
@terranceparsons51852 жыл бұрын
This is so simple and clever.
@tomwalker9965 жыл бұрын
I absolutely hate math and I can’t stop watching these videos... help!
@Doronoss Жыл бұрын
So cool! I showed it to my friends, I got beaten up.
@Aventium8 жыл бұрын
I got distracted and missed the first minute of the video. I thought this was a stack of random numbers and it was all a joke.
@ARidley9828 жыл бұрын
I kinda feel like calculating 11n by doing 10n + n is easier than doing this digit addition method, personal preference though.
@user-qb4ke6gm5b7 жыл бұрын
You should go over Pascal's triangle!
@TerraPupaAbyssus7 жыл бұрын
I've never known how to quickly multiply by 11, thank you so much!
I felt like the last part was a trick because you said that they could write their two numbers in any order. So reversing the 8 and the 5 means the function no longer works.
@sk8rdman8 жыл бұрын
No. If you reverse the order of the first two numbers then the 4th number, in this example, will be 21 instead of 18, and the following numbers will consequently also be different. All of the numbers after the 3rd will be different, and the end total will be different, but it will still be correct.
@casumma3 жыл бұрын
Hi There-on your chalkboard did you know that you actually inverted the order of the first two digits in your sequence? I’m no math genius, but I do believe that in a Fibonacci sequence it is the number 5 followed by the number 8. (0, 1, 1, 2, 3, 5, 8, 13...etc.) However, You wrote: 8, 5, 13, 18. This throws off all the subsequent sums. Shouldn’t it be instead: 5, 8, 13, 21, 34, 55, .... etc? (On the other hand, you have a great smile and telegenic personality)