Pure maths, physics, logic (braingames.ru): non-trade-related brain games - page 6

[moskitman]

Integer:

If any, any will do. The pyramid of Cheops, no.

and how is the location or shape of the pyramid of Cheops different from the others?

[михаил потапыч]

moskitman:

OK, let's rephrase:

what is the angle of ABC?

I claim it is 90 degrees.

The way you drew 90. Same as the base of the pyramid, but that's not how you measure an edge.

When measuring, you will have to measure 90 degrees at the measuring point on each edge and accordingly the points you have drawn on AB and BC will be lower and the angle will be larger.

To calculate, you need the ratio of the pyramid's height to its base.

[ALEXEY NIKOLAEV]

moskitman:

OK, let's rephrase:

what is the angle of ABC?

What difference does it make? I think you have to measure different angles to solve it.

[Vladimir Gomonov]

Mischek:

You will need the ratio of pyramid height to base to calculate

Yep.

[Anatoli Kazharski]

Here are the proportions of the pyramid of Cheops. )) Taken from here: http://www.magiclab.biz/ratios.htm

Size	Howard-Vyse	Tailor	Smyth	Petrie	Cole	Proskuryakov	Mercilaud
A Length Foundations	232,751	232,867	231,394	230,561	230,365	233,164	232,797792
H Height	148,153	148,133	147,113	146,721	146,731	146,595	148,061683
h Apotheme	188,395	188,415	187,158	186,592	186,539	187,300	188,33737
a inclination angle facet	51°51'	51°49'57"	51°49'	51°50'34"	51°52'06"	51°30'21"	51°49'38,25"
F=tg2a	1,620676	1,618623	1,616799	1,619834	1,622818	1,581158	1,6180340

[Andrey Dik]

Cheops pyramid

The Pyramid of Cheops, one of the three pyramids at Giza, is near Cairo and is built in the shape of a regular pyramid with a square at its base. According to an accurate reconstruction (it was partly dismantled into stone by the locals):

1. Base: Square with sides of 230.35 meters (b=230.35 m)
2. Height of the Cheops pyramid: 146.71 meters (h=146.71 m)
3. The lateral facet of the pyramid is an isosceles right triangle - the angle at the apex is 90o, the two angles at the bottom are 45o.
4. In total there are 4 triangular sides (of course, because the base is a square).
5. The pyramid is combined from cubic blocks of limestone, the greatest of which has length of an edge of 1.5 meters.
6. Probably, originally to the top of a pyramid led 210 steps

Golden Sections: Denote by c the length of the 'staircase' which is formed by the inclined side face of the pyramid. By Pythagoras' theorem:
c2=h2+(b/2)^2~186.52 meters (b/2)/c~0.618 golden ratio.

Later one more "Golden regularity" has been noticed: the area of the pyramid basis concerns the area of all 4 lateral sides of a pyramid in a proportion of "golden section". The area of a lateral side was equal to the square of its height (bc/2 = h2)

Here - the angle between two neighbouring sides is 112.13 g.

[Rustamzhan Salidzhanov]

http://forum.lah.ru/forum/44-3886-2

http://www.airpano.ru/files/Egypt-Cairo-Pyramids/1-1

https://www.youtube.com/watch?v=dlhauWG8F70&list=PL2853301A05168DCA&feature=plcp

[Dmitry Fedoseev]

moskitman:

OK, let's rephrase:

what is the angle of ABC?

I argue that it is 90 degrees.

96 degrees and a bit.

[Dmitry Fedoseev]

moskitman:
and how is the layout or shape of the Cheops pyramid different from the others?

There are also shallow tall pyramids there, I mean, upwards elongated, different proportions.

[Dmitry Fedoseev]

   double tpi=MathArctan(1)*8; // это пи
   double fi=(MathSqrt(5.0)+1.0)/2.0; // это фи, золотое сечение, 1,618 
   double ab=fi;
   double cb=1.0;
   double ac=MathSqrt(fi); // MathSqrt(fi*fi-1), удивительное равенство:)
   double cd=MathSqrt(2);
   double abc=MathArctan(ac/cb);
   double abcgr=abc/tpi*360;
   double adc=MathArctan(ac/cd);
   double adcgr=adc/tpi*360;

   double EathSmallR=6356.9;// 
   double EathLageR=6378.2;// 
   double Height1=(MathTan(abc)*EathSmallR-EathLageR);
   double Height2=(MathTan(adc)*EathSmallR-EathLageR);
   Alert(Height1," ",Height2);

For the edges to hit the poles, the pyramid must have an elevation of 1707.9017 km.

For ribs - the top must be at a depth of 660.4626 km.

Double-check if you are wrong.