@Mnemovice
I am using many different method for squaring numbers. And I am using base method for squaring number that is in 41 to 60.
Example - 53 is 3 more than 50 so I am adding 3 in 25 . And square the number that is I add.
53^2 = 25 + 3 | 3^2
= 28 | 09 ( in second part always be 2 digits)
47^2 = 25 - 3 | 3^2
= 2209
46^2 = 25 - 4 | 4^2
= 21 | 16
= 2116
59^2 = 25 + 9 | 9^2
= 3481
If you have any doubt than you can ask me.
I would square like this 53 squared = (50*56)+3 squared = 2809
There is now a follow up video with a bit more detail: Why These Are The Best Numbers | FOLLOW UP.
First of all; the video looks great!
However; calculation like it’s done in the video is not always possible.
As you are accustomed from me; a simple example.
In decimal 21 divided by 7 would be written as 11 divided by 7 in Iñupiaq.
Looks like this:
I do not see a way - like it is done in the video - how to do this division geometrically.
Then; let’s look at the example of the first elaborate division.
I’ll rewrite the division in easy to understand decimal:
(61 * 400 + 61 * 5 * 20 + 61) / 61
Since 400 is the third position, comparable to 100 in decimal and 20 is the second position, comparable to the tens in decimal, and the ‘5’ in the ‘61 X 5 x 20’ means it needs to be raised, it is easy to see that the number 30561 can be easily divided by 61.
Also in decimal - admittedly not as fast or beautiful as in the video - it is easy to see that 30,500 is 61 X 500. If not immediately visible, 61/2 = 30.5, so apart from the decimal point, the sequence 305 forces its way up if you half 61.
Or you can quickly do 61X5 = 305.
Of course the second example: 46,349,226 / 2,826 is indeed more difficult in decimal compared to Iñupiaq.
Indeed, this is a calculation that is easy to do geometrically.
However; change one number and try to do the calculation again:
Now, try to divide the number above by this:
(It is not impossible of course, just a lot more difficult).
So I grant that the particular properties of Iñupiaq gives one an advantage.
I also like the properties of writing the numbers. The base 5 inside a base 20 certainly has advantages.
Just don’t think it a is a system that will solve all your problems with arithmetic.
beautiful!!!
didnt know any such method existed, marvellous! and thank you
Hi Leo,
What do you want you say with the notes?
I see you scribbled numbers on the notes, in some kind of sequences.
Is there a message behind them?
Which techniques they use
How to show 2020 number in inupiaque
2020 = 5 * 20 * 20 + 1 * 20 + 0, so:
i have been doing like this
46^2 = 16-5| 4^2
16 is 4^2 and 5 is one less than unit digit of 46
do you have notes or collected information about how you do all of your calculation ?may be your blog or youtube channel ?
Can you mention the methods please…
I am going to revisit the second calculation in the YouTube video:
We would write it like this:
46,349,226 / 2,826.
We can transpose the Iñupiaq numerals to arabic numerals.
Iñupiaq numerals are from 0 to 19, so I will use the ‘|’ symbol as a separator.
Also I’ll add zeros to 0-9 to help with alignment.
The picture above transposes to:
14|09|13|13|01|06
divided by:
07|01|06
Let’s just do the division.
07|01|06 times two is 14|02|12.
Now subtract:
14|09|13|13|01|06
14|02|12|00|00|00 -
00|07|01|13|01|06
Answer is 02.
Now we can just subtract 07|01|06 (times one):
00|07|01|13|01|06
00|07|01|06|00|00 -
00|00|00|07|01|06
Answer is 02|01.
We subtracted from the 5th position (where we would put the ten thousands), the result starts in the 3rd position (where we would put the hundreds).
We could not subtract from the 4th position (since it is 00) and thus we add a zero to the answer:
Answer is 02|01|00.
Again, we can just subtract 07|01|06 times one:
00|00|00|07|01|06
00|00|00|07|01|06
______________________ -
00|00|00|00|00|00 This is zero. We are done.
Answer is: 02|01|00|01.
This is: 2*20^3+1*20^2+1 =
16000 + 400 + 1 =
16,401.
Seems to me that this is almost as easy as the example in the video.
