Egyptian and Chinese Math

originally posted by: onequestion

Wait.. do you have a video for that?

Um, no, I found that by myself.

That's fascinating. In my school days, we did short form multiplication/division with a single _|""""""""| box, then we'd do the long form. After that it was all about hexadecimal, decimal, octal and binary.

For me, I'd multiply 14 x 13 in my head as 14 x 10 (=140) + 14 * 3 (= 10 * 3 + 4 * 3 = 42) = 182

Here's a link to BBC Bitesize tutorials:

www.bbc.co.uk...

Good find sir!

It is things like this that makes the dumbing down of America all the more obvious!

a reply to: onequestion

They are actually teaching this method in schools these days. My son learned it in 3rd grade and continues to use it now i the 4th.

But they call it Lattice math, not Lettuce.

a reply to: onequestion



Back in the Day I remember I showed this "Demonstrated " too My Teachers At age 10 ( 1980 )

They were Amazed of being Shown a Different way of Thinking instead of a Times * table & Modern Division

Something Like the way of this Video Represented the 17 x 25 and the 1075 / 25

Yup The Power of 2

As this was Easier for me instead of the Times Table ..


They ask me Where I learned this .. I Couldn't give them a Reason Why or How I knew

I just Knew ...

IT may be a Longer Route to Some .. but if you have a Good Memory say ( Near Photographic )
it will be easier to do within time ...







So did the Pre Columbiains Aztec's Mayan's had the Same way of thinking ?

The Mayans Used a 20 System instead of the Modern 10

Mayan Mathematics and Architecture
www.dpsk12.org...

Maya Mathematics
www.michielb.nl...

Math in Ancient Civilization
math2033.uark.edu...

Hieroglyphics: Egyptian, Mayan, and Chinese Characters
www.tony5m17h.net...

Early Egyptian Hieroglyphic mathematics used decimal description, as we do now, and binary calculation, as do our computers. Their fundamental expansion of numbers was in terms of a power series in powers of two, using both negative and positive powers:

Counting and
Arithmetic of the Inca
etnomatematica.org...

originally posted by: Tucket
a reply to: onequestion
Really cool, but I found the egyptian method to be inefficient. I just tried to solve 89/538 using the Egyptian method and I found myself reverting back to the N. American method of multiplication just to find out the powers of 538. In the video its easy cause hes using easy numbers. Also, if I use the N. American way for this equation, im writing fewer numbers.

Very cool thread nevertheless, Ill give the chinese method a go.

I was taught the lattice method but never used it, I didn't watch the video here but I remember the concepts. I don't think it's that good because it requires a lot of space to write the problem out. Needing 1 additional line per every factor of 10 is very space efficient and that translates into reducing the paper used, and less time writing out the problem. Remember that the more time you have to spend simply laying the problem out, the more time you have to spend on each problem. Time to solve is pretty relevant in regards to viable methods.

originally posted by: onequestion
First of all why the hell wasnt i taught this in school? No wonder so many of them are becoming programmers in India and China. Makes sense they are teaching them how to do proper math. I want to learn how to do this.

This method works well on pencil and paper but only for smaller numbers, the larger you go the more space you have to use on the paper and the more time you spend writing, every additional column increases the size. You go from a 2x2 square (4) to multiplying 10's in a 3x3 (9), 100's in a 4x4 (16), and 1000's in a 5x5 (25), scale down if you're using decimals. It gets exponentially larger for each digit.

Personally, I find it useful to be able to convert binary to decimal as well as hexadecimal to decimal but I work with computers day in and day out. I don't actually think this Egyptian method is better for most applications and that's because the numbers we use every day are in base 10 while this method being taught is in base 2. Whatever you gain in having a simpler solution (and it's only simpler if you have paper) you lose in having to do the conversions. Most of us can't automatically equate 11 in binary as being 3 in base 10.

I'll teach you two more methods real fast. The first is what I use and what they're trying to teach in common core. The advantage to this method is that you can quickly solve problems in your head. The disadvantage is that you can't approach the problem in a straightforward manner. In order to multiply or divide you need to also add and subtract. Lets use an example of 73*529 (randomly picked those numbers, there's no significance to them).

The basics of this idea are that you factor the numbers to numbers that round to 5 and 10, I only use 10 but it's being taught today to also use 5. So 73*529 can also be expressed as (70*529)+(3*529). We can also round the 529 because 73*529 can be expressed as (73*530)-73. Using both of those principals you can express 73*529 as ((70*530)-70)+((3*530)-3). If that's not simple enough you can take it a step further from this point and write it as ((70*500)+(70*30)-70)+((3*500)+(3*30)-3). This problem might look more complicated but if you're trying to compute it in your head it is far easier to solve. This equation evaluates to ((35000)+(2100)-70)+((1500)+(90)-3) which then evaluates to (with some reorganizing) 35000+2100+1500+90-70-3. That then becomes 37100+1500+20-3 which is then 38620-3 and finally 38617. It might seem unwieldy at first but once you get used to it, it is actually very easy to evaluate expressions this way. I'm regarded by most math people I meet (math majors, computer scientists, and people that hit calculator buttons really fast) as having exceptionally fast and accurate computational ability, this method is a large part of why that is, I quite literally use it hourly if not more.

The next thing I want to show you goes back to binary, it's a technique known as bitshifting and is a way to multiply or divide by powers of 2 quickly. Computers actually do this to save CPU cycles in order to optimize. If you go back to the video you posted the presenter goes through some basics of how binary is represented. We'll take a typical 8 bit (1 byte) unsigned value which ranges from 0-255. Lets use 173, that would be expressed in binary as 10101101:
128 - 1
64 - 0
32 - 1
16 - 0
8 - 1
4 - 1
2 - 0
1 - 1

Now, if I want to divide that number by 2, excluding the remainder I can just move all of the bits 1 to the right, with the right most bit falling off (multiplication moves it 1 to the left, and if you run out of space a value also falls off... which would be an insufficient memory error in the case of a machine, but here we could just add a 256's column). That means 10101101 becomes 01010110. If you convert that back into decimal form.
128 - 0
64 - 1
32 - 0
16 - 1
8 - 0
4 - 1
2 - 1
1 - 0

And then add that up you get 64+16+4+2=86 which is 173/2 or 86.5 (becomes 86, there are no decimals in binary). Using this technique a computer can multiply or divide by powers of 2 (2, 4, 8, 16, 32, 64, 128, 256, etc) very very quickly. If you wanted to divide by 4 instead you would shift 2 to the right, or by 8 it would go 3 to the right. Using the 173 example again 10101101 becomes 00010101 which if you write out is 21
128 - 0
64 - 0
32 - 0
16 - 1
8 - 0
4 - 1
2 - 0
1 - 1

And if you calculate it out 173/8 is 21.625 which truncates to 21.

This type of bit operation is the fastest operation a computer can do actually. If you're interested further in this, there's a relatively famous application of it in the collision check Quake 3 Arena which allowed the game to perform some very advanced lighting and reflection techniques. Here's the wiki page.

Most compilers and interpreters will automatically bitshift if possible these days so you don't have to expressly tell a computer to do it, but I do a good deal of math when trying to optimize my code that can take advantage of faster math like this (among other techniques).

originally posted by: onequestion
a reply to: Grovit

Im looking for an easier method for fractions im hoping they have something for that too because i need it for my job.

If you come across anything let me know.

It all depends on what you're using the fractions for. I don't know much about construction, if you're more descriptive I might have a suggestion, but most of the fractions I deal with are for probability so there's no guarantee. For example are you trying to multiply fractions together, are you adding them, do you simply want to convert from a fraction to a decimal?

To add on to the above, I've now watched the lattice videos and can once again echo what I said about it being slow due to the setup time. I could solve each problem in my head before the boxes were even drawn. The lattice method is a neat trick, but it's impractical for just about everything.

Right. This works. sure. But it seems faster to do the math as taught in standard public school. Just about 1/10th of the time it takes to draw out a lattice system. Although, I admit folk learn using different methods. Whether visual learners or auditory, which is a difference learnt (at least to me) prior to even a multiplication table. Personal preference I assume. Unless dealing with binary, which is altogether above and beyond me.

Mind Blown on the Egyptian math video at about the 3:20 mark!

It just seems to translate so perfectly in my mind. And how can I knock a system of communication that was good enough for the Voyager mission....

Math was always my worst subject in school - I always had difficulties in Math so I kind of just gave up and got the credits I needed to earn my diploma. If I had been taught a different way, I could quite possibly have my name on a pyramid by now!

originally posted by: harlot7
Math was always my worst subject in school - I always had difficulties in Math so I kind of just gave up and got the credits I needed to earn my diploma. If I had been taught a different way, I could quite possibly have my name on a pyramid by now!

Here, not exactly high level skills or anything but I was just doing something quick. Your name on a pyramid, it's even 8 sided like at Giza.
www.dropbox.com...

a reply to: Aazadan

I love it - Thanks!!!!!!! I will use it.

I feel as if there is something inherent with these other teachings of mathematics! Just totally clicks in my mind.

originally posted by: harlot7
a reply to: Aazadan

I love it - Thanks!!!!!!! I will use it.

I feel as if there is something inherent with these other teachings of mathematics! Just totally clicks in my mind.

There's the occasional bit of wisdom but they weren't really all that advanced. For example the Egyptians had no system of decimals, they represented decimals as fractions. That's why their usage of PI that you can measure in the pyramids is 22/7.

The best way to get better at math isn't to learn a technique that provides some fundamental clarity. It is to take courses on logic and to do a lot of math problems. Find something interesting to you that you can apply math to and start learning. My past two big hobbies (combined going back to 1999) have both been math heavy dealing with algebra and probability and professionally I use geometry/trig almost non stop, so I have an interest in them too.

The more math you do, the better you'll get.

Good find, Not good in maths I have to try this thank you for the videos

Thanks for the links. I'm gonna go home and teach this to my kids. They already excel in Math, but this should push it over the top.

originally posted by: amicktd
Thanks for the links. I'm gonna go home and teach this to my kids. They already excel in Math, but this should push it over the top.

If your kids are young teach them binary. Just like foreign languages it's easier to learn when you're young before you have an established thought pattern. It may or may not pay off but if they take a job in the future that's heavy on the computer math they'll be glad they know it.

For that matter, if they excel in math teach them some computer programming. Python is the best beginner language because it's not very verbose. It's among the most valuable skills a person can know. My personal prediction is that the hottest job 15 to 20 years from now will be either graphics or AI programming.

Different ways of finding the number you need. I like these. Math can get really difficult but with several techniques to use finding your result can be less encumbering.