The height of the pyramid of Cheops

  • Context: News 
  • Thread starter Thread starter Ad VanderVen
  • Start date Start date
  • Tags Tags
    Height Pyramid
Click For Summary

Discussion Overview

The discussion revolves around the height-to-base ratio of the Pyramid of Cheops, exploring different mathematical interpretations and historical measurements. Participants examine the implications of using the golden ratio versus a ratio derived from geometric principles, while also questioning the accuracy of ancient measurements.

Discussion Character

  • Debate/contested
  • Mathematical reasoning
  • Conceptual clarification

Main Points Raised

  • Some participants present calculations suggesting that the height-to-base ratio of the Pyramid of Cheops is approximately 0.6366 based on geometric principles, while others propose a ratio of approximately 0.6180 based on the golden ratio.
  • One participant questions the validity of the first calculation, emphasizing the uncertainty surrounding ancient measurements and suggesting that both ratios might be equally valid within a certain margin of error.
  • Another participant expresses skepticism about the significance of the golden ratio, labeling it as numerology and suggesting that the calculations may lack meaningful context.
  • There is a proposal that modern measurements could provide a more accurate ratio, potentially using replicas of the pyramid for precise calculations.
  • Some participants note the historical context of the pyramid's construction, indicating that the Egyptians may have had specific intentions regarding dimensions and angles.
  • Clarifications are made regarding the mathematical expressions used to derive the ratios, with some participants asserting that the calculations are straightforward while others find them confusing or arbitrary.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the validity of the calculations or the significance of the ratios. Multiple competing views remain regarding the interpretation of the ratios and the reliability of the measurements.

Contextual Notes

Participants highlight the limitations of ancient measurement techniques and the potential inaccuracies in historical data, suggesting that any conclusions drawn from these calculations should consider these uncertainties.

  • #31
russ_watters said:
omeone had to stick their neck out to pick the new angle.

Literally.
 
  • Like
Likes   Reactions: Rive and russ_watters
Mathematics news on Phys.org
  • #32
Vanadium 50 said:
The Giza pyramids have slopes of 42, 43.3 and 41.6 degrees. (Slope taken from the corners to the top).
You clearly have looked into this more than I have; all I have is what the wiki article says:
wiki said:
Slope51°52'±2'
https://en.wikipedia.org/wiki/Great_Pyramid_of_Giza
And:
Wiki said:
One Egyptian pyramid that is close to a "golden pyramid" is the Great Pyramid of Giza (also known as the Pyramid of Cheops or Khufu). Its slope of 51° 52' is close to the "golden" pyramid inclination of 51° 50' – and even closer to the π-based pyramid inclination of 51° 51'. However, several other mathematical theories of the shape of the great pyramid, based on rational slopes, have been found to be both more accurate and more plausible explanations for the 51° 52' slope.
https://en.wikipedia.org/wiki/Golden_ratio

Can you explain the discrepancy?
V50 said:
Literally.
You did what I saw there.
 
  • #33
Slope is "rise over run", right? The rise is well defined, but the run is not. I took them from the corners. Wikipedia takes it from the midpoint of the sides, presumably.
 
  • #34
From the wiki article on "golden ratios" I cited in an earlier post also referred to by other posters:

Eric Temple Bell, mathematician and historian, claimed in 1950 that Egyptian mathematics would not have supported the ability to calculate the slant height of the pyramids, or the ratio to the height, except in the case of the 3:4:5 pyramid, since the 3:4:5 triangle was the only right triangle known to the Egyptians and they did not know the Pythagorean theorem, nor any way to reason about irrationals such as π or φ.[99]

Bell, a noted mathematician and historian of mathematics, debunked many popular misconceptions surviving into the 20th Century and, apparently, well into the 21st.
 
  • Like
Likes   Reactions: BWV
  • #35
Vanadium 50 said:
Slope is "rise over run", right? The rise is well defined, but the run is not. I took them from the corners.
Oh...that's an interesting choice.
 
  • #36
For some reason, this thread reminds me of this:

dimensional_analysis.png


(source: https://xkcd.com/687/)
 
  • Haha
  • Like
Likes   Reactions: f95toli, Rive and BillTre

Similar threads

Undergrad Determine ## \beta ## as a function of ##\theta## linkage
  • · Replies 2 ·
Replies
2
Views
2K
MHB Possibilities for the side and angle of the triangle
  • · Replies 10 ·
Replies
10
Views
3K
Discrepancies In Clebsch–Gordan Calculations (Dipole Transitions)
  • · Replies 0 ·
Replies
0
Views
1K
Undergrad Optimization problem with multiple outputs: impossible?
  • · Replies 6 ·
Replies
6
Views
3K
High School Having trouble deriving the volume of an elliptical ring toroid
  • · Replies 4 ·
Replies
4
Views
4K
1D Particle & Energy w/ F(x): Am I doing this right?
  • · Replies 7 ·
Replies
7
Views
2K
Area of segment cut from a circle
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Possible simple formula for ellipse circumference
  • · Replies 6 ·
Replies
6
Views
3K
Undergrad Which of the two answers is correct?
  • · Replies 7 ·
Replies
7
Views
2K
Graphing the Superposition of Two Standing Waves
  • · Replies 8 ·
Replies
8
Views
2K