The Barone Pyramid ... need help

[Don Barone]

Hi all

Here is my favourite triangle (pyramid). What I need to know is what the base length is ... EXACTLY !

As a note the red circle is exactly tangent to the enclosing triangle.

Anyone's help would be greatly appreciated.



It scales to just over 52 degrees and this image shows the same result but it is not the result I am hoping for.




Thanks in advance

[Don Barone]

Well I finally figured it out thanks to a great website.



And here is the website - The inscribed circle in the triangle

My solution was 213.90 ... pretty darn close for scaling off a drawing.

Here are my diagrams ...







Pretty clever for an old feller

[Don Barone]

And a formula so I will never forget ...

Cheers

Don

[Don Barone]

Okay what does all this tell us ? Firstly my perfect Wood Pentagram has been shown, I am sad to say, that IT DOES NOT FIT into the Great Pyramid. I needed 213.9 as a diameter and I got 213.825. Close but not nearly as close as I needed. So I went about trying to find out what I needed to make it fit.

Through trial and error I determined that in order to get the height at 280 and the diameter of the circle at 213.9 the base needed to be 440.24 cubits. But that would mean we would have a cubit of 20.60 inches as 9068.4 (average) / 440.24 = 20.5988 or 20.60 rounded off.

This would make all my other research wrong and I wasn't about to accept that. As I always do I calculated the angle of 280 / 220.12 and found that this would give us 51.8276. What is very interesting is that the Phi angle is 51.8273 almost exact and then I realized something, something that I think has not ever been proven before. In order for The Great Pyramid to represent and show us Phi then the inscribed circle must be Height / 1 + sine of 18 or 1.309017 or in this case 280 / 1.309017 = 213.901. After exhaustive testing I found that this is not possible with the Great Pyramid unless we go over 440, so in actuality we need 440.24  and thus once and for all I think I have shown the Phi is not, sadly and unfortunately not part of the design of The Great Pyramid. Trust me I am distressed.

So the Phi Pyramid would have to be Base = 440.24 and Height = 280 and this then would give us a pyramid of 9068.4 inches for the base and 5767.654 inches as the height with a 20.60 inch cubit. There is no other way Phi fits. Case closed I fear.

db

[Don Barone]

We can still get Phi but we have to use 440 as a base and 279.844 as the height and this would give us a diameter of:

440 x 279.844 = 123131.502073

Slope = sq root of 220 squared + 279.844 squared

Slope = sq root of 126712.664336

Slope =  355.967

Slope + Base = 575.967

Diameter = 123131.502073 /  575.967

Diameter = 213.782 ( x  1.309017 = 279.844 and proved again)

So in a Phi triangle or pyramid just divide height by 1.309017 to get diameter of inscribed circle.

db

[Don Barone]

... and this is very, very interesting. If we use 440 and 279.844 to get Phi we get this ...

9068.4 / 440 = 20.61 inches per cubit

and now for the height ...

279.844 x 20.61 = 5767.58484

and thus we have the amazing fact that 280 x 20.5985 EXACTLY EQUALS 279.844 x 20.61 both equaling 5767.58484 (inches)

So the Phi Pyramid would have to be Base = 440.24 and Height = 280 and this then would give us a pyramid of 9068.4 inches for the base and 5767.654 inches as the height with a 20.5985 inch cubit. There is no other way Phi fits.

This is indeed a new wrinkle to our problem

[Don Barone]

Error correction.

The average base is 9068.8 NOT 9068.4 THUS 9068.8 / 440.24 = 20.5997 and much closer to 20.60. thus 280 x 20.60 = 5767.91

279.844 divided into 5767.91 = 20.6111562642 ( x 440 = 9068.91 )

and from Petrie ...

So Petrie allows a height of from 5769 to 5783 inches. Oh my the endless possibilities !

In this image he also puts down the size of the remaining blocks at the top of the pyramid which we will look at next.

5769 gives an angle of 51.83286 while 5776 gives us 51.8666 and finally 5783 gives us 51.900 so the angle could be anywhere between 51.832 and 51.900 ... 5773.377 gives us the Pi angle and finally 5767.846 would give us The Phi angle. ... Hmmm the waters are pretty murky methinks.

db