



The Great Pyramid of Giza contains a mathematical marvel. It defines ‘Squaring the Circle’. The height of the Great Pyramid can be used to construct a circle (whereby the height of the Pyramid is the radius of the circle), while the base of the Great Pyramid can be used to construct a square. 



The perimeter of the square is equal to the circumference of the circle. Squaring the Circle based on equal circumferences. See also my article Squaring the Circle  a clarification in which I show that there is no difference between StC based on circumferences and StC based on surface areas. The Squaring the Circle (StC) happens because the angle of the sides of the Great Pyramid is 51.85 degrees (or 51.51 in degrees and minutes). So, where do we find 42? Inside! 



Although the outline has this strange angle of 51.85 degrees, the all important inner diagonal angle is exactly 42 degrees. The Math showing this can be found further down this article, but let's first have a look at 42. You can approach this angle of 42 in a different way. You can start with 42. So, let's do that. First we take a isosceles triangle with 42, 42 degrees. 



Then we take a second identical triangle and place this triangle perpendicular to the first triangle.




We now have created the skeleton of the Great Pyramid. You likely didn't know it is that easy to construct the Great Pyramid. With creating the skeleton of the Great Pyramid, we also have constructed a situation that defines Squaring the Circle. With other words, the number 42 is directly related to Squaring the Circle. In my book ‘the Organizing Principle’ I explain and show the importance of Squaring the Circle. How it is a core element of our existence. You could even call Squaring the Circle, the Shape of Spirit, and as we have seen, the number 42 is directly related to this. The answer is 42. 

The Math 

Let's start with the outline of the Great Pyramid and let's assume that the length of its base is 10 units. 



That means that the perimeter of the constructed square is 4 * 10 = 40 Since the Great Pyramid defines ‘squaring the circle’, the circumference of the circle is also 40. The formula 2πr ( 2 * pi * radius) expresses the relationship between the circumference of a circle and its radius (r). This radius (r) is in our situation the height (h) of the Pyramid. In other words... The circumference = 2 * π * radius (height). Or... Radius (height) = circumference / (2 * π) In our example... height = 40 / (2 * π) = 20 / π 



The earlier constructed square (from ‘squaring the circle’) is identical to the floor of the Pyramid, which has four sides of 10 units each. Using the theorem of Pythagoras (A² + B² = C²) we can calculate the length of the diagonal. Since A = 10 and B = 10, it follows that the diagonal squared = 10² + 10² = 200. From this follows that the length of the diagonal is ⱱ200, or ⱱ100 * ⱱ2, or 10 * ⱱ2. 



The length of half a diagonal (d) is 5 * ⱱ2 The tangent of the angle we are looking for is the height (h) divided by half the diagonal (d). Or tan(angle) = h/d = (20/π)/(5ⱱ2) = (4/π)/ⱱ2, whereby... 4/π = 1.2732 ⱱ2 = 1.4142 So, tan(angle) = 1.2732 / 1.4142 = 0.9003 To find ‘angle’ we have to use arctangent. The arctan(0.9003) = 42. Or, the ‘angle’ = 42 degrees. 

Like I said before, in my book ‘the Organizing Principle’ I explain and show the importance of Squaring the Circle and how it is a core element of our existence. You could even call Squaring the Circle, the Shape of Spirit, and as we have seen, the number 42 is directly related to this. The answer is 42 © Bert Janssen, 2024 

Please join me on my and lets investigate! 