Multiplication Tables Are Taught Wrong

Let me explain how multiplication tables are often taught wrong, and show a bunch of underrated patterns within them:
0:00 - Part 1: Metamemorization
2:26 - Parts 2 and 3: Primes and Composites
5:58 - Parts 4, 8, and 9: Squares and Almost-Squares
13:30 - Parts 10 and 100 and etc: The Beauty of Zooming Out
19:40 - Part Infinity: Conclusionfinity
Thanks for watching! Leave a comment about your favorite part. And consider showing this video to a teacher in your life (if teachers incorporated more of these patterns when teaching arithmetic, I don’t think as many people would hate multiplication tables!).
If you want bonus content, I've been doing livestreams every few days on my ‪@Domotro‬ channel, which are saved like videos on that channel's "live" tab afterwards.
This episode was directed/edited/soundtracked by me (Domotro) and was filmed by Carlo Trappenberg, with some additional filming help from Raphael Matos and Andy Sykora.
Special thanks to Evan Clark and to all of my Patreon supporters:
Max, George Carozzi, Peter Offutt, Tybie Fitzhugh, Henry Spencer, Mitch Harding, YbabFlow, Joseph Rissler, Plenty W, Quinn Moyer, Julius 420, Philip Rogers, Ilmori Fajt, Brandon, August Taub, Ira Sanborn, Matthew Chudleigh, Cornelis Van Der Bent, Craig Butz, Mark S, Thorbjorn M H, Mathias Ermatinger, Edward Clarke, and Christopher Masto, Joshua S, Joost Doesberg, Adam, Chris Reisenbichler, Stan Seibert, Izeck, Beugul, OmegaRogue, Florian, William Hawkes, Michael Friemann, Claudio Fanelli, The Green Way, Julian Zassenhaus, Bailey Douglass, Jan Bosenberg, Brooks Boutwell, David Irvine, qe, George Sharabidze, Jack Dwyer, Fredrik, and Dave Brondsema!
Check out the Combo Class Patreon at / comboclass
If you want to mail me anything (such as any clocks/dice/etc. that you'd like to see in the background of Grade -2), here's my private mailbox address (not my home address). If you're going to send anything, please watch this short video first: • You Can Now Mail Me Th...
Domotro
1442 A Walnut Street, Box # 401
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If you want to try to help with Combo Class in some way, or collaborate in some form, reach out at combouniversity(at)gmail(dot)com
In case anybody searches any of these terms, some topics mentioned in this episode include: times tables / multiplication tables, memorization vs. learning patterns, square numbers, almost-square numbers such as pronic numbers and numbers of the form n^2 - 1, graphs such as y=n/x, number factors, where numbers of different amounts of digits live on the times table, number theory, random fun math facts, a few arithmetic tricks, feeding some squirrels, and more!
Disclaimer: Do NOT copy any dangerous-seeming actions (which were actually performed in a careful way) involving fire, tools, or other chaotic activities you may see in Combo Class episodes. This is an episode of a show that is purely meant to provide entertainment and education. Also, do not copy the squirrel-feeding without doing research, since if you feed wild squirrels in certain habitats, it will actually be bad for their diet and hunting skills in the long term.

[@ComboClass]

Let me explain why multiplication tables are often taught wrong, and show a bunch of underrated patterns within them: 0:00 - Part 1: Metamemorization 2:26 - Parts 2 and 3: Primes and Composites 5:58 - Parts 4, 8, and 9: Squares and Almost-Squares 13:30 - Parts 10 and 100 and etc: The Beauty of Zooming Out 19:40 - Part Infinity: Conclusionfinity Thanks for watching! Leave a comment about your favorite part. And consider showing this video to a teacher in your life (if teachers incorporated more of these patterns when teaching arithmetic, I don’t think as many people would hate multiplication tables!). If you want bonus content, I've been doing livestreams every few days on my @Domotro channel, which are saved like videos on that channel's "live" tab afterwards. There is also a Combo Class "Discord" where combo lords chat, and a "Patreon" for those able to help fund future episodes (see the video description for names of my supporters and links to those).

[@MarloTheBlueberry]

My favorite part? This whole dang channel!

[@cbrooksusmc]

Love how dude just randomly feeds a squirrel in the middle of shooting.

[@jerrys2292]

And it makes it into the final cut

[@junipre985]

its his pet squirrel

[@hansisbrucker813]

That squirrel surely does recognize a nutcase 😂

[@Exantho]

one of the few people on the internet who can manage to scratch my itch for entertainment pertaining to mathematics

[@TheDsyr4MyDmyz]

Who are the other few? The more entertaining math channels I know, the better

[@AnoNymous-dh2sv]

Dude this is literally the most entertaining mathematics channel in history, and I've checked most of them for years. It's clearly underrated (or at least I hope it's the people interested in mathematics who are few keeping the subs low for its quality).

[@marossedik2130]

When I found out about the almost square numbers being very similar to square numbers, I tried doing my own research generalizing the pattern and extending it more down the line. The pattern would go: a²=(a-n)*(a+n)+n² which can be really useful if you needed to calculate something like 28*32, as 30*30 is easy and going 4 down leaves you with 896...

[@tristantheoofer2]

this is actually exactly what i do sorta lol. like if its 8*11 i just do 11*11 (121) then subtract the first numbers (11 and 8) in my head, so 3. then multiply that by 11 (33) then subtract it from 121. 121 - 33 is 88

[@r4masami]

There is a mental math book that explicitly teaches this method for trying to calculate the squares of 2 and 3 digit numbers, it is where I first learned the idea

[@9nikolai]

@@tristantheoofer2 Isn't it better to make multiples of ten or other even numbers rather than changing it into a bunch of primes?

[@abbe1255]

@@tristantheoofer2 that's a lot of calculations for multiplying by 11 when you could just do 11*n=10*n+n

[@JNCressey]

for looking up info about this, this identity is called "the difference of two squares"

[@Budjarn]

These videos are soothing to me. The chaos makes me feel safe and welcome, like it’s okay for me to be messy.

[@ND62511]

Every upload I watch is more chaotic than the last. Regardless, it is really cool to see the times table with some new perspective. Lots of cool patterns exist in it, as is the case for all mathematical structures!

[@tegxi]

One of my favorite examples of patterns being more useful than memorization is trig identities. I may forget that tan^2 + 1 = sec^2 but I do know the definitions/practical meanings of sin, cos, tan, and I know how they relate to csc, sec, and cot, so I can figure it out from there!

[@RichConnerGMN]

nice pfp

[@TymexComputing]

This is how Squirrel obesity starts.... - squirrel obesity makes squirrels spherical instead of squareical

[@Giguv05]

Squirrecal

[@stickmcskunky4345]

This general idea of teaching by way of showing what patterns exist, indicating where they overlap in different representations, and then extrapolating that pattern outwards.. it's fire. It's very broadly applicable as so many patterns are overlapping and relatable across so many systems and compositions. One commenter mentioned that the only problem with teaching kids this way is that it's too much at once. I disagree to the extent that I believe that most humans, and especially some, are geared towards recognizing patterns and then seeing how they fit together and finally extrapolating what the broader system looks like.. we *want* to see how it fits together and our biology backs up that drive. There could be no foul in exposing young curious minds to some of the fundamental overarching patterns in many arenas, and I'm in agreement that it's probably the thing to do in fact.

[@xaropevic7918]

An interesting property of square numbers that I always forget but find cool is a thing that I remembered this video is that if you pick a number, let's start simple with 1 and 2, then square it, so we get 1 and 4, then subtract the bigger one with the smaller one, we get 3, then we repeat the process with the bigger becoming the smaller number and its successor, so 2 and 3, then squaring it, we get 4 and 9, then we do 9-4 and we get 5, which is 3+2, and we can repeat that process a lot of times (for example 16-9=7, 25-16=9, 36-25=11, 49-36=13, 64-49=15 and so on)

[@Lilly-Lilac]

It’s also very interesting how these “multiplication tables” generalize to other operations. Tables like these are incredibly useful for representing the abstract notion of function composition with regards to groups and their actions (and many other places, but I found it very helpful in that case.) Noticing patters akin to the square numbers or primes etc can give you a much better idea of the group you’re dealing with.

[@EnderMega]

Not only hes talking about a good topic but he is one of the few channels I saw that *actually has a personality.* Please, dont stop, we need more people like you.

[@watcher314159]

There's actually a general case for the (n+1)(n-1)=n²-1 type of "almost square" that I actually find really useful. (n+x)(n-x)=n²-x². So 6×2=(4+2)(4-2)=4²-2²=16-4=12. And indeed, if you continue moving diagonally away from the squares on your multiplication table you'll see this pattern of subtracting swuares quite clearly. And what I mean by finding this really useful is that if I have to, say, multiply 40×46 in my head, I'll often find it easier to find the square of 43 and then subtract 9 from it. Not that I have 43² memoried, but I can work my way up from 40² (which is 4²×10²=16×100=1600). (n+1)²=n²+2n+1 after all, so I just add 81+83+85=(80×3)+(1+3+5)=249 to 1600 for 43²=1849, and thus 40×46=1840. Yeah, sure, I could also do 40²+(40×6), but often I personally find the "almost square" method reduces the number of things I have to keep in memory all at once (and also the fact that they use different operators, plus the ability to add on my fingers rather than doing even more mental multiplication, helps me avoid mixing things up). It's not always the right tool for the job, but it's a tool I've found to be worth knowing (it's also one of the first bits of math I derived from first principles without any help as a kid (without even using algebra), so I have an admitted soft spot for it).

[@louierichardson4750]

Stopping me forgetting my entirely memorised education and teaching me more interesting and useful ways to apply more solid concepts... I wish you were my maths teacher sooo bad

[@JNCressey]

I tend to have a few sparse multiplication results memorized to act as waypoints, then move to the desired multiplication with repeated addition.

[@lexdeobesean]

This dude gives me very strong Radagast the Brown vibes 🤣👍

[@ofconsciousness]

For real!

[@aComedicPianist]

There are two things I’ve discovered in this video by looking at the times table: The difference of consecutive same-parity integers happens perpendicularly to the perfect squares diagonal and symmetrically from the perfect squares diagonal until the difference becomes 0, reaching the outer edges. This relates to the other thing: The sum of same-parity integers form diagonals parallel to the perfect squares diagonal, but they’re offset by the integer they start on and are the addition of the same parity of that integer.

[@Roxor128]

I never properly memorised my times-tables. I fill in the gaps with addition or subtraction, depending on whether the closest value that comes to mind is above or below what I need. One thing nobody taught me about times-tables as a kid, but I realised when studying computer science at uni, and that I wish more people knew about, is that they're an example of the space-time tradeoff in action. It's a lookup table, trading increased memory for reduced compute time. You're spending a hundred slots in your memory to save the time you'd otherwise spend calculating those commonly-used values. For an actual use in a real program of such a technique, transparency in Duke Nukem 3D uses a 256*256 2D lookup table to find which colour in the game's palette should be used for a 1/3 transparent pixel (or 2/3 by swapping the order) when overlaying transparent walls or sprites. The actual calculations of what colour you'd get with a 2:1 mix of any two colours in the game's palette, and which colour in the palette was the closest match to it, was done by the developers during development and saved to a file that the game can then load from disk on startup. It takes 64KB of memory at runtime, which is not insignificant for a game that has to run on machines with 8MB of memory, but it's much faster than calculating three linear interpolations and then searching through the 256 palette entries for the closest match. Definitely worthwhile if it means you can run the game on a 486, rather than a Pentium.

[@romasissues]

Thank you for making brilliant free educational content. The atmosphere and manner of teaching is so comforting and wholesome. I am hooked.❤️‍🔥

[@peppermann]

Absolutely , less memorising times tables and more patterns and intuition. Another great video ! 😊❤️👍

[@PotatoSofi]

The only problem with teaching kids exactly like this is that it presents way too many concepts at once. The best way to first ever present a times table to a kid is as an addition table, showing different patterns with sum and subtraction on the times table, then presenting the division one as the perfect opposite. After all that, it would definitely be benefical to slowly present some of those concepts you showed here and quite a lot of those would be useful for future concepts.

[@ComboClass]

I agree it shouldn’t be this fast paced if teaching a kid, you’d want to spread these patterns over the course of different days and spend time having the kid “discover” them and ask questions about them, instead of giving all these answers right away

[@RichConnerGMN]

nice pfp!

[@MarloTheBlueberry]

I absolutely love this channel. You do such a great job at teaching! Keep it up!

[@flamephlegm]

I feel like the filming has leveled up a bit and the aesthetic is really coming together with all of it. Exciting seeing shit start to really gel! As always the math is high quality infotainment, thank you D!

[@maynardtrendle820]

Man- this is SUCH a good maths channel! Great job, brother!😊🎉

[@Fidtz]

Great video. I suspect the going up to 12 thing is a tradition from a combination of Imperial measurements, old school British/Roman currency with 240 pence to the pound in 20*12 units and some time based calcuations.

[@cs8712]

"Hello 911? I need to report a fire next door - oh wait...he's just doing that thing again...nevermind"

[@morgunkorn_]

i love how this gives a new perspective on things taken for granted. also, SQUIRREL!! 🌰🐿

[@Escviitash]

And the pattern, as shown in the 3 * 5 example, continues. For all numbers their product is: the average, squared - the distance from the average, squared e.g 7 * 4 Average = (7 + 4)/2 = 5.5 Distance = (7 - 4)/2 = 1.5 (5.5)^2 = 30.25 (1.5)^2 = 2.25 30.25 - 2.25 = 28 = 7 * 4. It extends to all real numbers, no matter the signage. e.g -7 * 4 Average = (-7 + 4)/2 = 1.5 Distance = (-7 - 4)/2 = -5.5 (the same absolute values as for 7 * 4, but swapped) 2.25 - 30.25 = -28 = -7 * 4

[@1495978707]

2:10 Our brains *love* patterns. That's like the whole reason we evolved intelligence, pattern recognition. Even a dumb butterfly can memorize a location across the world. But smarter critters can and enjoy making deductions and noticing patterns. Crows are fascinating for their ability to do so

[@DocWorm]

The squirrel bits were so good holy shit. The times when you were pointing to things on the times table desperately needed highlighting though.

[@SteinGauslaaStrindhaug]

I have ADHD, so I stubbornly refused to memorise anything... I "cheated" by figuring out "tricks" to avoid actually remembering the tables, like times x * 2 is just x + x and x * 5 is just (x*10) / 2 and x * 10 is simply adding a trailing zero etc. Which means rather than memorising; I figured out what multiplication actually means.

[@SteinGauslaaStrindhaug]

Still slow as heck doing multiplications in my head, even with single digit numbers. With the exception of times 2 and times 5 because dubling and halving is so common in my work as a programmer that I have over time involuntarily memorised them through repeated exposure.

[@stirlingblackwood]

Domotro is a legend. He should make a second channel where he proves everything from his main videos 😎

[@ComboClass]

I have a second channel haha (@domotro) although it’s not always for proofs, I mostly use it for shorts and livestreams and random extra content

[@ker0356]

15:19 I absolutely adore this cozy way of doing math on paper. Sure, computers can make accurate pictures, but it feels almost soulless

[@emilyrln]

Sharing this with my parents, one of whom is currently teaching 5th grade and the other of whom is a teacher's aide specializing in math for grades 3-8 or so!

[@custard4189]

Ive been coming up with fun tricks for multiplying things by 15 because every morning when I make coffee I use a 15:1 coffee:water ratio by weight in grams! a fun little exercise every morning :)

[@juh9870_projects]

That squirrel is my spirit animal

[@PersonallyOptimistic]

You're honestly a fantastic educator

[@Thezaccazzac]

You Positively Exude Witchy Energy. From your disregard for current conventions, to your attunement with nature and your urge to breakdown and understand the world you reside within. People like you are who generate improvement around the world.

[@zelda.1129]

This turned out to be unexpectedly very cool!

[@stalfithrildi5366]

As a secondary school maths teacher in the UK, I often get pupils who have struggled to memorise all the tables. I get them to memorise the squares and work from there to get 8x7 etc as its the exact method that got me thru to Post Grad studies.

[@LoZander]

Here's s fun thing i never thought about before: if you make a rectangle from with a corner in upper left corner of the product cells, and the opposite corner at the lower right corner of some cell with number n, then n is the area of that rectangle, and the two coordinates are describe the side lengths of the rectangle. I don't know why ive never considered that before.

[@ofconsciousness]

This genius is a dark mage of our time, resurrecting the ancient power of math and conjuring a future where it's no longer feared, but embraced by the masses. These videos are mildly terrifying in the best way - the kind that strikes awe, reverence, and a burning curiosity soaked in eager urgency.

[@grantraynard]

Love your lab or studio, It design seems timeless 😅

[@DanF8]

wow reversal of entropy in the first 20 seconds - must be a powerful episode

[@Jethro_Sigwilder]

Domotro - Explainer of Maths, Patron of Squirrels

[@TymexComputing]

very nice - there are chineese combo classes where children are taught multiplying quickly (like a quick reading, tapping pencil) i am awaiting children that will be using Parseval theorem better than i :)

[@pasixty6510]

The biggest real life benefit of this video goes to the… you guessed it… yeah… to the squirrel 👏👌😹

[@johndickinson82]

I found that polygonal numbers form straight lines, like square numbers but different slope. Triangular numbers like 6, 10, and 15 are all in a line

[@ComboClass]

I have been planning some episodes about polygonal numbers for a while, which I’ll film before too long. They have tons of amazing patterns

[@kzdjarrard]

I love polygonal, polyhedral and shape forming numbers as a whole! I look forward to your video on them.@@ComboClass

[@EvilSandwich]

The difference of squares trick is my favorite way to make people think I'm smarter than I actually am. By my ability to "effortlessly calculate" that 58 x 62 is 3596. Or 29 x 31 is 899. I'm not literally crunching the numbers in my head, I'm just cheesing the rules lol

[@davekachel]

I love this backyard scientist aesthetic

[@R.B.]

I hadn't considered the almost square factors before. Looking at those diagonals reveals difference of two squares. If you know your square numbers, fanning out from them orthogonally, you just subtract square numbers for the distance from the square diagonal. That fact alone helps you figure out half the numbers in the table. As for your curve, I think it might be more clear to say greater than 100 or greater than 10. This is because you aren't going to start counting at 0 for that band, 0 being a special case. Not only will it improve the appearance of the curve, but it makes more sense logically.

[@codatheseus5060]

Yep, ive got the 12x12 times table memorized from 3rd grade still Now ive got the times table (cayley table) for the sedenions which are defined by 15 imaginary axis which each square to negative one (for 15 different directions for rotation) and 1 real axis for scaling. Technically every single combination of elements of the 15x15 sized cayley table exists for some setup for sedenions, because you can change whether the element squares to negative one or positive one, and the fact that their names are entirely arbitrary. The setup i have memorized is equivalent to a matrix with the format (reals) (along the diagonal), -i, -j, -k, ... (i being the standard imaginary numbers, and you have all of them one after the other along the first row all negative) then all the imaginaries go in their respective antidiagonals and when they cross the regular diagonal they switch to positive versions of themselves. The rest of the items are actually super easy to figure out because the pattern you got from filling out the first half with the information ive given you

[@frank.e.underwood]

Most things fallen in any video of yours I've watched :) Once I memorized the primes up to 199, I felt like I could intuitively calculate all the other numbers in the cells. I memorized them because I like to count primes when I do breathwork, or am in line waiting for something, just as some fun for my brain. I never would've done it at a teachers request because I'm that kind of stubborn. Primes are the gateway drug to numbers. Math could be so fun in school if they let it be.

[@ofconsciousness]

Thanks!

[@tristantheoofer2]

yo domotro so that curve you found in the times table i think is called an asymptote (but its offset by abt 1 in each direction). i could be wrong tho but yeah

[@SuperIdiotMan00]

I think by the end of Grade -4 the entire video will be a giant Rube Goldberg machine on fire.

[@morgangraley1049]

Get you a guy who caresses you like Domotro caresses almost-square numbers.

[@philj9594]

It seems complicated to people, but imo using patterns is infinitely more easy than rote memorization of the entire table. In fact, it blows my mind that people actually do that. I actually didn't even learn with a table. I just gradually picked up on various patterns myself as I progressed through math. Idk why, but my school didn't even use times tables for the gifted class. Only the regular class was forced to memorize them. I guess they just assumed we'd pick it up naturally? They were right, but I think most people really don't even need the table to get good at it.

[@illumina-t-info]

this is how I learned, i never learned math the right way and learned patterns

[@hurktang]

Thank you! now instead of doing 7x13 i can do 10x10 -3^3 because I learned that squares are squares away in the other diagonal. Can I do the opposite? like 14x14 is 10x18+16 ? Nice!

[@aguyontheinternet8436]

4:50 ok that is just adorable

[@4thalt]

will there ever be a combo class video where nothing falls, breaks or gets set on fire?

[@scragar]

As a kid I never memorised the times table, I just remembered every 3rd entry. I don't need to remember 1×7, it's obviously 7. I don't need to memorise 2×7, it's obviously 7+7=14 3×7 I memorised 4×7 is just 3×7+1=21+7=28 5×7 is 6×7-7 = 42-7=35 6×7 I memorised 7×7 = 6×7+7=49 ... Memorising 144 different answers never made sense to me when I can remember about 30 and never be more than two simple addition/subtractions away from the answer. I also never liked history. So many dates to memorise and they were just meaningless to me.

[@andrewgarcia6951]

Love the maths... My PTSD is allergic to the banging. Will try with volume off and CC on. ❤❤❤

[@skaruts]

Now that was unexpected! And pleasantly so. :)

[@0Shitou]

Let's say you are asked to multiply two numbers which are not far away from each other. I'll take the Example with 21x28 First step: find the "middle number" between 1 and 8 middle number is either 4.5 So you can select anyone you want but I'll select always de smallest one; 4 in this case. Then 21x28 = 24x24 + 24 - (28-24)*(28-23) Thus: 24x24 + 24 - 4*3 Now, I dont know how much 24x24 is but I do know that: (a+b)² = a² + 2ab + b² hence: 24x24 = 20² + 2*20*4 + 4² And finally, 21x28 = 20² + 2*20*4 + 16 +24 - 12 = 20² + 188 = 588 If the two numbers are too far away like: 21x51,then: 21x51 = 21x25*2+21 and calculate 21x25 as 23² - 4 = 20² + 2*3*20 + 9 - 4 = 400+120+5=525 So: 525*2+21=1071 With Practise you can do this mentally pretty fasy

[@nihilisticgacha]

I learned the multiplication table in chinese (up to twelve), and it sounds sort of like a chant since it has only one syllable for the numbers 0 to 10. i'm at the point of my life at which i rarely do mental arithmetics and old memory starts to mutate, one day I realised that my muscle memory of reciting the multiplication table betrayed me after double checking the calculation with a calculator, because it sounded right even though the numbers are wrong

[@yanntal954]

This table is the reason why we should have all converted ourselves to being base 2 creatures. That way we would've only had to "memorize" the truth table of the AND gate!

[@Blaineworld]

pattern i found and used as a dumb baby: for 9 times a single digit number n, the tens digit is (n - 1) and the ones digit is (10 - n)

[@piciaxel]

there may be one other interesting way to actually teach multiplication tables better and that is by counting since the connexion is a bit clearer between the factors of the same number then again, for some children even the dice representations that you were showing might help since the current memorization is so dry

[@tsjbb]

That squirrel shot was cool

[@ComboClass]

If you liked the first squirrel shot you are in for a treat because that squirrel (and/or it’s family) returns through the episode and other recent episodes

[@antimatter7258]

i cant even physically imagine how dirty that entire setup must be

[@koko969w]

This channel is lit

[@asailijhijr]

He keeps the squirrel away by throwing clocks at the ground.

[@DeOxygenation_]

19:42 I legit thought he took a bite out of a tennis ball

[@meesvandenberg9468]

Fire, squirrels and math! What more do you need?

[@ronanclark2129]

I thought this was an Explosions & Fire video because of the thumbail with the fire, lab coat, and face

[@lucasbrelivet5238]

In France, we only learn tables up to nine. By the way, I don't really see how those patterns with the inverse function are useful, especially since we don't learn about functions and graphs until long after memoizing the times tables.

[@DanDart]

Domotro: "What's 12 x 7" Me, proving his point: "84-FUCK"

[@ComboClass]

Haha. Maybe I should have picked a larger example, but yeah that is an example of the type of calculation that I think people shouldn't worry whether they have "memorized" or not, since it's quick (and maybe even good for the brain) to calculate 7(10)+7(2) in your head.

[@DanDart]

The way I was taught included tricks to aid in memorisation, but ended up memorising the answers anyway, because of easy shortcuts like this. Never have I been taught "It's like that, you have to remember it this one way, just because." - they did indeed make it as easy as it should be for me.

[@mujtabaalam5907]

How does zero appear an infinite amount of times in the 0-9 table?

[@zippydipity42]

It's good to see that the mad hatter has found a hobby.

[@JuliusUnique]

here in germany we only had to remember the quadratic numbers up to 20, so only the diagonal, not the rest, thankfully

[@RohitKulan]

I think I have it memorized to 27. I don't know why though.

[@hkayakh]

In school, my teacher would have us answer times tables very quickly and if you got a certain amount right, you’d move up a rubber band color. The colors went something like red, then orange, yellow, green, blue, purple, brown, white, black and so on. It was very fun.

[@tristantheoofer2]

for us in 2nd grade we did this thing where we got tested on our multiplication up to 12*12 and if we got em all right before a certain day (i was the first one since my skill in math is fucking ridiculous), i think the beginning of the next year (so january 2018) we got a pizza party thing. it was awesome

[@michaelwinter742]

Time stable? I bet you love this.

[@theneoreformationist]

I actually had a moment the other day when I wished I memorized the multiples of 13, knowing I could have solved something much faster.

[@Censeo]

As a dart player I accidentally memorized the three times table up to 20

[@alikaperdue]

product = (sum/2)²-(diff/2)² product = average²-(average-smallest)² consider sum = a+b, diff = a-b, product = a×b, average = sum/2, smallest = a, for numbers a

[@pretentiousjackal]

19:43 Is he trying to grow a cubic apple on the tree, in the plastic case? Or is it a message in a bottle?

[@3s843a]

i learned somethin'!

[@vilvd3934]

That intro sounds crazy

[@RiteOfSolaris]

I was taught all this aswell though.

[@TalsBadKidney]

Hey howya doin combolords

[@DanjinSpear]

Why the fuck wasn't I taught maths like this at school.

[@MxGx]

Yay

[@alikaperdue]

If two large numbers are close to any easy square, then they can be multiplied using a quadratic. solve: 999,996 × 999,997 let m = 1,000,000 999,996 × 999,997 = (m-4)×(m-3) = m²-7m+21 = 10¹²-7×10⁶+21 = 1,000,000,000,000-7,000,000+21 = 999,993,000,021 easier than multiplying for real. * any numbers separated by two is the square of the middle minus 1. or (x-1)(x+1) = x²-1

[@mistafizz5195]

Bro sounds like Vsauce2 and looks like Jack Harlow.

[@phi0_]

Damn just found you. You should get a lav mic cause when you turn away it can get harder to hear you.

[@ComboClass]

Yeah I’ve been testing out some different audio options for future episodes. I do want my voice clearer but don’t want to lose the bird/nature sounds in the background haha

[@phi0_]

​@@ComboClass Well my audio expertise ends with "better mic = better sound"

[@freesov]

might be worth exploring a multiple mic option if you decide to dig into it - because, yeah, definitely want the ambient noise to stick around

[@tinypileofpolydimethylsiloxane]

i like you clock wizard guy

[@RichConnerGMN]

nice pfp

[@hansisbrucker813]

Aren't the part numbers ordinal? Wouldn't that mean that the last part isn't ∞, but ω? 🤔

[@echoawoo7195]

Dude you're like the Disney Princess of Mathematics !

[@echoawoo7195]

Disney Princess confirmed, I saw that smile !