Why 440 and 280 for the dimensions of The Great Pyramid ?

[Don Barone]

Hi all ...

Thanks to Mark Hammond I have come to a realization on why the numbers 440 and 280 could have been used for the dimensions of The Great Pyramid ... As always I get an idea from someone and then build on their ideas so full marks and credits go to Mark Hammond for spotting the first number, 440 while I will take credit for the second number 280 ! Mark has a very interesting blog or website which I will link to here ... Mark Hammond's website on The Great Pyramid

To save time I will simply borrow one of Mark's images to speed things along.  Please be advised that the following image is copyrighted to Mark Hammond !!!!! In it he very cleverly shows the way 440 can be arrived at in a pyramid. Here is the image ...



So off I went to bed thinking about this image. And as I was laying there I was thinking to myself well I wonder if we can fit 280 into this idea. And as I lay there I started doing calculations in my head and finally came up with this idea. I immediately got up and came to this idea and I present it in the image below.  I have checked online and could not find another image of this idea so for the present I will take full credit pending proof that it is just an old idea that I have rediscovered ... But it really is quite clever ...



Now I stopped at 70 and 280 simply because I wanted it to fit into the 280 cubit height for The Great Pyramid but what is really interesting is that each line adds up to the square of the numbers minus the 0 so that we have 1, 4, 9, 16, 25, 36, and 49 and we can continue on to infinity in this way and always we get get the next square in the sequence. For example if I had gone to 80 the line total would have been 640 and is of course 8 squared or 64. 

Anyway I thought it was pretty clever ....

Cheers
Don Barone



 

[Don Barone]

In the image ...



I may be more clever than I thought for the number of actual digits, totally disregarding the value of them amazingly also total the number to the right . So for example we have in the top row 1 digit, in the second row we have 3 digits, in the third row we have 5 digits, in the fourth row we have 7 digits and when added together yield the corresponding number to the right ... Actually quite neat ...

Cheers
Don barone

   

[Don Barone]

Okay having trouble sleeping as numbers keep dancing through my head and was thinking about how each successive line gave us the next sqaure and then this occurred to me. It would seem that the square of the next number can be calculated by simply adding the next successive ODD number ... Probably old hat but it had never occurred to me before . Case in point ... Let's take the odd numbers up to 25 to start with ... they are

1
3
5
7
9
11
13
15
17
19
21
23
25

Now the first square is 0 + 1 = 1 and square of 1

Next we would add 3 to this to get 4 and 2 squared

next we would add 5 to this to get 9 and 3 squared

next we would add 7 to this to get 16 and 4 squared

next we would add 9 to this to get 25 and 5 squared

next we would add 11 to this to get 36 and 6 squared

next we would add 13 to this to get 49 and 7 squared

next we would add 15 to this to get 64 and 8 squared

next we would add 17 to this to get 81 and 9 squared

next we would add 19 to this to get 100 and 10 squared

next we would add 21 to this to get 121 and 11 squared

next we would add 23 to this to get 144 and 12 squared

and finally we add 25 to this to get 169 and of course 13 squared

As I said probably old hat but I had never noticed this before ... or at least had forgotten I knew it ...

Cheers
Don Barone

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[Don Barone]

Okay more fun with numbers ... noticing the above sequence of adding the odd number led me to this observation.

Here is a very quick and easy method for figuring out the total value of a sequence of sequential numbers ...

For example what if we wanted to know the value of adding all the numbers up to 47. Seems like it would take a while but actually it is amazingly simple. But first let's try it with a lesser number ... say 5 So what are the numbers when we and 1,2,3,4,5 together we get 15 ... here is what we do ... first we square the number to get 25 then we subtract the number to get 20 then we divide by 2 to get 10 and then add the number back on to get 15.

Let's try another one let's try 13. so we square this to get 169 then subtract 13 to get 156 then divide by 2 to get 78 then add 13 back on to get 91 so adding 1,2,3,4,5,6,7,8,9,10,11,12,13 together should give us 91 and indeed it does !

Now 47 ... 47 squared is 2209 then subtract 47 gives us 2162 now divide by 2 to give us 1081 and then add back on 47 to give us the result of 1128 !

So now let's try a tougher one ... say 59 ... we simply square 59 to get 3481 then subtract 59 to get 3422 then divide by 2 to get 1711 then add back on 59 to arrive at 1770. So adding all the digits from 1 to 59 together will give us 1770.

Again probably old hat but I had not given it a lot of thought before ...

Cheers

Don Barone

[Don Barone]

As I suspected ... old hat ...

There’s a popular story that Gauss, mathematician extraordinaire, had a lazy teacher. The so-called educator wanted to keep the kids busy so he could take a nap; he asked the class to add the numbers 1 to 100.

Gauss approached with his answer: 5050. So soon? The teacher suspected a cheat, but no. Manual addition was for suckers, and Gauss found a formula to sidestep the problem:

sum from 1 to 100:

100(100 + 1)
------------- = 5050
        2

Oh well ...

Cheers
Don Barone

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[Don Barone]

Okay trying to have a nap but it is not working so I have been thinking about this ...

When you multiply ANY TWO SEQUENTIAL NUMBERS and then divide by 2 the answer will give you the total of all the digits added together up to the lower number ... and then by simply adding the higher number you have solved for both numbers ...

Example 76 and 77

76 x 77 = 5852 then divide by two and we get 2926

So 2926 is the total of all the number up to and including 76

by simply adding 77 to that (2926 + 77) to get 3003 we have solved for the total of all digits up to and including 77

Very neat trick ...

Cheers
Don Barone

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