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## The base line

The base line's length is taken from the Survey data of William Petrie who reported that the average length of the four sides of the Great Pyramid was 230.348 m to an error margin of ± 1.27 cm (± 0.0055%). This base line is highlighted and shown in green on the interactive drawing, and the object information panel for 'Line B' shows that this surveying measurement is faithfully reproduced in the geometry.

From this base line the ellipse can be formed, and to facilitate this a formula for the circumference of an ellipse is required. The mathematician Srinivasa Ramanujan discovered a remarkably accurate formula for calculating an ellipse's circumference when the ellipse in question is almost circular, as is the case with the Earth's polar cross section. When Ramanujan's formula is applied to the Earth it produces a value for the polar circumference of the planet which is accurate to one sixtieth of the diameter of an hydrogen atom - in other words absolutely perfect. Click here to show Ramanujan's formula.

By using Ramanujan's formula in reverse, the lengths of the axes of an ellipse can be determined from its circumference.

### Creating the ellipse

Starting by comparing the surveyed base length to the half circumference of the Earth, the scale of the model of the Earth can be determined as being 1 : 86842 ± 5 and from this scale the ellipse's 'a' and 'b' radii can be determined from the formula above. Click here to highlight the ellipse and show its object information panel.

Once the length of the radii have been calculated, then the geometric height of the pyramid can be determined as 146.40 m (twice the semi-minor axis of the ellipse). Petrie's surveying gave the height of the pyramid as being 146.71 m ± 0.18.

With a base length and geometric height to the building having been determined it must be possible to now determine the face angles of the pyramid geometrically because the end points of the base line and the apex of the structure, which is the upper turning point on the ellipse, are known.

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Last edited: 3rd July 2019
Last code/graphics edit: 29th March 2021