I don't think that's the case. Weirdly enough, I think it's a coincidence.
Who would use circumferences of a wheel in one axis, but diameters of a wheel for another?
See...have you ever laid out a roof? Here in inch land, the slope of a roof isn't given in degrees, it's given in rise over run, and run is typically 1 foot or 12 inches. So a slope of 45 degrees works out to 12 in 12, it rises 12 inches for every 12 inches. You'll find a lot of American roofs have a 33.69 degree angle. Why that weird number? It's a slope of 8 in 12.
Pause for the Europeans to cope with being carried through the industrial revolution by the English and Americans by pontificating about metric. Are we done? Good. Moving on.
The ancient Egyptians didn't have feet and inches, they had cubits, palms and fingers. Four fingers to a palm, seven palms to a cubit. The Egyptian unit of slope is the Seked, palms of run per cubit of rise. Notice that: We're now in run over rise, not rise over run.
The first (attempt at a) smooth sided pyramid is the Bent Pyramid built for Sneferu. It starts off at a Seked of 5, which works out to a smidge over 54 degrees. The popular lore is the building started showing cracks, so to save weight they reduced the slope to a Seked of 7.5, which works out to 43 degrees. The nearby Red pyramid, also attributed to Sneferu and apparently built immediately after, is built entirely at that 43 degree angle.
The pyramid at Meidum, Sneferu's other pyramid, was first built as a stepped pyramid like Djoser's, and then modified into a smooth sided pyramid, with a Seked of 5 palms, 2 fingers, or about 51 degrees. This worked, at least in antiquity (the Meidum pyramid is heavily ruined in the modern day).
So when his son Khufu decided to build the biggest pyramid of all time (and nobody has proven the magnificent bastard wrong yet), that's the slope he used. 5 palms, 2 fingers. 51 degrees.
So the ratio of the Great Pyramid's height to the distance from the center to the middle of a base edge is 7 to 5.5. That means the ratio of the height to the length of a base edge is 7 to 11. Which means if we take the length and width of the pyramid's base, and divide it by the height, we just so happen to get 22 / 7, which about a millennia later the Greeks would discover is a pretty good approximation for Pi, but the 4th dynasty Egyptians didn't know about that.
That's not what Khufu's son Khafre did. Khufu was a magnificent bastard but Khafre was clever sumbitch. Khufu built the world's biggest pyramid. Khafre built his slightly smaller pyramid uphill from his dad's so his would look bigger. And, he built it very slightly steeper, with a Seked of 5.25 (about 53 degrees). That works out to the same slope as a 3-4-5 triangle. 3/4 is 0.75, and because Seked is given as palms per cubit we multiply by 7, 0.75 * 7 is 5.25. And they DID know about that in the 4th dynasty. Clever sumbitch.