The Maths of Ancient Egypt: Numbers, Calendars and Geometry in Architecture

Oxford Mathematician Dr Tom Crawford explains some of the maths used by the Ancient Egyptians - from their number system and calendar, to the geometry of their magnificent architecture. Filmed on location in Egypt.
The video was inspired by an article discussing the 8-sided nature of the Great Pyramid of Giza, and how the concavity would affect its volume. This is explored in the third part of the video via a calculation of the volume of a square-based pyramid, and how that would be modified for a step-pyramid such as the Pyramid of Djoser at Saqqara.
The first part of the video looks at the number system of the Ancient Egyptians, including the meaning of the hieroglyphs and how they multiplied numbers together using a method of continuous doubling (or binary). Tom visits the wall at Karnak Temple which contains carvings of the numbers.
The second part of the video explores the Ancient Egyptian Festival Calendar and the division of the year into 3 seasons of 120 days. Tom visits Kom Ombo temple which contains the only known example of hieroglyphs detailing the transition to the new year.
The third and final part of the video looks more closely at the architecture of tombs such as the Pyramids and the Valley of the Kings. Tom visits both sites, as well as the ancient city of Saqqara. The volume of a standard square-based pyramid is calculated and compared to that of a step pyramid, with a rather surprising result.
Produced by Dr Tom Crawford at the University of Oxford. Tom is Public Engagement Lead at the Oxford University Department for Continuing Education: www.conted.ox.ac.uk/profiles/...
With thanks to:
UCLA Digital Karnak
Quora
Robin Spivey
NASA
Penn Museum
Wikipedia
Bassano Ltd
For more maths content check out Tom's website tomrocksmaths.com/
You can also follow Tom on Facebook, Twitter and Instagram @tomrocksmaths.
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[@TomRocksMaths]

Let me know if you like this new style of video and I'll see if I can make more :)

[@mathsaccount-fb5kb]

Can't wait to see!

[@deliciousrose]

It's interesting to see the systems used by ancient people outside of western world, I think a lot of them have unique and fascinating symbols and counting methods. Would love to see more of them and some bits of fun facts about the maths.

[@Rack979]

Ancient Babylonian math would be a great topic for the next video!

[@febobartoli]

Lovely stuff! Sad to say the maths you’ve been doing lately is a bit much for me, so this was an easy video to watch while working out.

[@Eudaimonia88]

Absolutely wonderful. More please! How about the maths used in Ancient Greece? The mathematics used to build the Parthenon would be super interesting.

[@matejcataric2259]

This is why I like this channel do much. Always new and interesting stuff and I am never bored. Well done Tom!

[@TomiThemself]

More Egyptian Maths, pwease!

[@emilyrln]

I love the combination of math and history in this video and would happily watch more in this vein!

[@robertorgan6037]

Loved the format and loved the content! You explain things very clearly. It was easy to follow along. Very enjoyable!

[@danitajaye7218]

LOVED this video! Excellent way of teaching and sharing information. Well done!

[@ahmedebrahim1754]

This is really wonderful that I'm from Egypt and I would like to thank you very much for this work, and I know nothing about these symbols

[@antoniomoyacatalan1746]

Such a great vid tom keep it up

[@DuncanBooth]

Nice to see they had spreadsheets in ancient Egypt. If we include the damaged cell that was skipped from that initial column of numbers the 128 is simply the total of the numbers above it. Pausing the video I can see it looks like that's the case for very column. I wonder what the column headings say?

[@Eudaimonia88]

Super cool content. More please for your long-time admirers! ❤

[@thegameroh-le3xb]

i am so happy u visited my countryyy love u bro best math channel ever

[@dru4670]

Loved this at 5 am!

[@dennisestenson7820]

Do you take your history for granite? Cool video.

[@whig01]

It's very simple they timed their calendar to the Sirius cycle as we do today.

[@501Mobius]

That is correct. The added extra days were just a shorthand. They would have to recalibrate their calendar at some point to have Sirus rise in the east at a certain date.

[@TheGmr140]

Really cool 😊

[@cosmoluc]

I'm sure you must be sick of comments like this by now, but I've become more confident knowing I'm better at multiplying 120 by 12 than an Oxford mathematics professor (15:06). I loved the video, by the way!

[@scragar]

12*120 is 1,440 not 1,460. Can't tell if you got it wrong or there's an adjustment in there because it's actually slightly less than a quarter of a day which does matter in the scale of a thousand years.

[@ingiford175]

Yep, saw that also. 12 x 12 is a gross (114)

[@deltalima6703]

@ingiford175. Wrong! Might want to look again. 😂

[@ingiford175]

@@deltalima6703Bah, doubled the 1 not the 4.... even the correction is not correct... Bah bah

[@kellerkind6169]

@@ingiford175his result was a bit gross too though ;-)

[@SgtSupaman]

It's just a calculation error. If he were truly accounting for the difference there (with the actual portion missing from each year being about .2422 days), it would take around 1,507 years for the calendar to be off by an entire year.

[@rmandra]

Thanks -- fun vid

[@SpokenWord4]

I enjoyed your video. Is there anyway you can show of Math was based on the one decimal system ( arithmetic, astronomy, and geometry). I met a guy in my younger years that showed me how easy it was to use the decimal system to calculate large amounts of data. I have forgotten but now have the passion to learn it again. Egyptian mathematics should be taught in school systems.

[@drziggyabdelmalak1439]

Wow!

[@iugoeswest]

Subbed!!

[@mitsaoriginal8630]

Their calendar was developed from kush at an ealier period. A large protion of their knowledge, is said to have originated from taseti south of the nile valley, deep into congo 12000+ yrs ago predating the sphinx.

[@oldreddragon1579]

I think 120 years times 12 is 1,440. I'm not good at mental math so I make mistake like that way more than I would like. Great information in any case. BTW Is it possible that the Ancient Egyptians used tokens to represent numbers so calculations could be done at speeds comparable to using an Abacus?

[@belleringr6377]

I love Egypt 🇪🇬 😊😮💪

[@Shahin-m]

Very interesting! At 33:11 minutes, you showed, from bottom to top: 0.256, 1.024, 2.304, 4.096 . Those multiplied by 1000; are 2 to the powers of 8, 10, 11 and 12; but instead of 2.048 we see 2.304!

[@lordofthe6string]

Came here to point the same thing out. Also, 2304 is 2048 + 256. Very weird but super cool.

[@kellerkind6169]

Thats because he messed up at the last step of the pyramid. the factor of the area was 0.5 (step 5 vs. step 6), but he devided 1.024 by 4 (-->0.256) instead of 2, which would have been 0.512 and thats where the 0.25 are missing.

[@phiefer3]

@@kellerkind6169He didn't mess anything up. The scaling factor for the last step of the pyramid is 0.5^2, just as all of the scaling factor for all of the other steps was squared because both the dimensions of the base are scaled down by it. The powers of 2 are somewhat coincidental, they arise from the fact that the scaling factor for the 2nd and 3rd steps are 0.8 which is a power of 2 with the decimal shifted, so at that point we have 8^4 ignoring the decimal shift. Also note that we only got the same scaling factor for both of these steps because the bottom layer has a different height while the other layers have the same height. Then when we do the next layer the scaling factor is (3/4)^2, we don't get a power of 2 this time because of that factor of 3 in the numerator; but in the next layer the scaling factor is (2/3)^2 and the 3s in the denominator cancel out the 3s from the previous layer and returns us to a decimal shifted power of 2. And then the last layer has a factor of (1/2)^2 which again keeps us on a decimal shifted power of 2.

[@NazmulHasan-zu5jt]

Hello sir, I'm from Bangladesh 🇧🇩

[@helenamcginty4920]

Back before decimalisation we had £s d. (Latin of course for pounds, shillings and pence). Where 12 pence made a shilling and 20 shillings made a pound which was counted in tens. Why so many older English people claim to find decimals difficult when we grew up adding money using 3 different bases depending on which column we were adding. No problem.

[@Firebird1005]

Liked this one. Pyramid math without mumbo-jumbo

[@dianafu2006]

:)

[@juliannaruffini]

ok just translated it. You see a list of festivals and the requirements for each festival for example bread

[@david.hilbert1234]

The country of Alexandria Euclid 🙌🏻

[@steveOCalley]

Tom, do it easier! Take the ideal smooth pyramid and add on the steps, 50 m2 x 12. Oh,wait, 3 dimensions, never mind. It’s good that I wasn’t an Egyptian engineer in a past life.

[@Atadistance70]

Secret to the pyramid is sacred geometry and sacred numbers and plasmoid power

[@emilywong6923]

The Inca used base 60.

[@triple_gem_shining]

Seems tedious 😂

[@mickeytaiwan]

The Egyptians loved dividing things like beer and bread…haha.. :-)

[@science0064]

India pls

[@satishgupta2658]

No

[@science0064]

@@satishgupta2658 😡😡😡

[@mechtheist]

Interesting note, the year 2000 was a leap year, which you might think it should be but no, years divisible by 100, the century years, are NOT leap years. SO, you add a 1/4 of day, then subtract 1/100 of a day, which is .24 hours, helpfully about a quarter of an hour, but wait, 2000 is a century year, why a leap year? So years divisible by 400 are back to leap years, so a quarter of that quarter of an hour added back, about a 4 minute correction.

[@SgtSupaman]

Yes, the actual length of a solar year is about 365.2422 days. This requires some weirdness in how a calendar has to handle it over long periods of time. So it becomes adding a day every four years until that winds up being so much more than what is needed that you have to skip adding a day for one of those years, but then doing that at the same interval will make you undershoot, so you have to proceed to add a day on one of those years you would have skipped, but doing that at the same interval for a long enough time will cause you to overshoot again, and it just goes on like that. Nature just doesn't care about clean math.

[@mechtheist]

@@SgtSupaman Actually, it doesn't go on like that, the last correction is good for only a 4 minute error over 400 years, 2000 was only the second of those 400 year corrections needed, so we're at most a few minutes off the exact year, nothing to worry about for a _long_ time.

[@SgtSupaman]

@@mechtheist, you contradicted yourself there. "Nothing to worry about for a long time" means there will eventually be something to worry about, which is exactly what I was talking about when I said "it just goes on". The periods of time by which these adjustments have to be made definitely get longer and longer (and we, personally, won't be around for them), but they still exist. I mean, we are trying to rectify what is likely an irrational number by adding in whole numbers where necessary. That will never work out evenly.

[@mechtheist]

@@SgtSupaman What I meant was that the 400 year correction was the last correction built into the calendar. Thinking about how the 'true' length of a year might be some irrational number really won't work since irrationals imply infinite precision but years are going to be variable, don't know what the magnitude of that is but of course, it's infinitely more variable than an irrational number. As it is, it will be roughly 6000 years to be off an hour and no one will care what the calendar has to say at that point, either we'll be gone or back to the stone age or will be diaspora-ed to the stars won't give a shit. Edit: Forgot to mention the day varies at least a second every few years, they keep adding leap-seconds to the time and that will screw up any irrational matchup also. Edit2: Forgot about the precession of the axis of rotation of the earth, that's gonna mess with the year to some degree but my brain hurts too much to think it through.

[@SgtSupaman]

@@mechtheist, yes, the variability of it occurred to me as well, but, again, you aren't really arguing against anything in my comments. Being variable doesn't in any way preclude each one from being irrational. I mean, given that there are infinitely more irrational numbers than rational ones, it is extremely unlikely that any variation of the solar year's length will be a rational number. But talking about whether or not someone will still care about the calendar thousands of years from now is purely speculative. I'm just talking about the math.

[@Incognitooo0815]

Tom *_KANN DAS !!_* One of the, so not to say *_THEEE_* most largest and at same time youngest maths profs of all times !!

[@rpow6861]

0:20 that isn't the great pyramid

[@andirijal9033]

Matematic lecture handsome and seksi

[@shapourmehrkar-asl1845]

12x 120= 1440

[@deltalima6703]

Volume is wrong. Pyramids have tunnels inside of them.

[@homegame-ls3ty]

yeah, like 0,07 %.

[@gameexplorert]

7 x 99 = 7 x 100 - 7 Just sayin'

[@uf9d_]

I am a Arab , can I study in Oxford ? , but can't speak English 😂

[@uf9d_]

I am in middle school and the mathematics curriculum is very difficult and includes calculus and integration space geometry. I have to study in Oxford, it's running in my veins

[@Crazy_mathematics]

Try hindu mathematics

[@satishgupta2658]

There is not Hindu mathematics

[@Crazy_mathematics]

@@satishgupta2658 who said ?

[@Crazy_mathematics]

@@satishgupta2658 who are aryabhatt ,bramhgupta, Bhaskara , Madhava and .... Who is shrinivasa ramanujan who said " an equation had no meaning for me unless it expresses the thought of God (goddess namagiri )"

[@Crazy_mathematics]

And this all discovered by me!!! A student of STD 12th who is studying mathematics from "A synopsis of elementary results in Pure and Applied mathematics (1886) G S Carr " book use By S Ramanujan to do self study of Mathematics

[@deltalima6703]

STD? Sexually transmitted disease?

[@christopherellis2663]

😂 10²/11²= 4/5= 500/625

[@TomLeg]

12 * 120 years is 1440 :-) ... never do mental arithmetic on camera

[@categorygrp]

the swallow lipsmack noise he makes when talking makes this channel so hard to watch

[@theworldofwoo8320]

Hard to watch, guy looks like he should be making coffees in a Seattle Starbucks. And then Antifa after work.

[@briankleinschmidt3664]

Math does not have an s at the end. Your teacher had a lisp. Besides there is only one math that encompasses all others - geometry.

[@nope24601]

Has anyone told you that you lose respect with those tattoos? I suspect no, and I wish someone would have told you sooner.

[@tomspoors768]

The tattoos are all maths related so let's judge people by the content of their characters, not the colours of their skin.

[@kaiserruhsam]

@nope24601 has anyone told you that you lose respect with that shallow prejudice? I suspect no, and I wish someone would have raised you better.

[@helenamcginty4920]

Maybe we can stop insulting the original commentator. He or she might be older, like me, and brought up in a very prescriptive 1950s Britain. We werent considered to be suitably dressed without a hat and gloves. Dressed for church older girls and adult women would have had matching hat, gloves and handbag. The mid 60s things started to loosen up. Tatoos were also working class. Even today you rarely hear a regional accent from news readers etc. Now I dont like his hair. I didnt even notice his tatoos. But then I've hung out with lots of people with weird hair, tatoos, and even vegans so I saw that he is a maths professor so respect.

[@kaiserruhsam]

@@helenamcginty4920 if OP is old they've lived through all that social progress and have no excuse.