My own favorite example of this is how the pyramids (and all the advanced trigonometry required) were built by the Egyptians prior to their discovery of the wheel
There's a ratio involving pi between the base lengths of the pyramid and its height. This is been interpreted by enthusiasts that the Egyptians knew about pi.
But, consider a measuring wheel, where you can mark off distances very accurately by counting revolutions of the wheel, say, 1 cubit in diameter (I know, I know, what's a cubit?). Then, if the height is laid out in cubits, the ratio of pi is there while being completely ignorant of it.
> This is been interpreted by enthusiasts that the Egyptians knew about pi.
Well if you want to calculate the circumference of earth and know the distance between Alexandria and Syene, where the sun casts no shadow at noon during the summer solstice, you also need to know pi.
If you know the angle and the distance between the two cities, you can just multiply the distance by [full circle divided by the angle], and that's the circumference.
Even if that were true, it wouldn't disprove the link to racism: Eratosthenes was Hellene, not native Egyptian. He "counts as white"; ancient Egyptians may or may not.
The pi ratio is strong evidence that a wheel is used somewhere in their surveying tools.
When I was a boy, I asked my mom how the Egyptians made their pyramid foundations straight. Without looking up from her book, she replied "pull a string tight". Then I thought I'd trip her up with how they made the foundation level. Without hesitation she said "dig a trench and fill it with water."
Most civilizations discovered. No one care about a wheel. The wheel itself is useless. Not everyone discovered the axle though, and even less created roads.
I have responded to a sibling comment with more information or examples. I hate this because I don't care about pyramids or Egypt, but I feel myself compelled to respond, I'm so sorry it's not against you, It's a recent pet peeve.
The 'wheel' itself was discovered everywhere. Round things are easier to move, but you need an axle to make it useful. And roads or flat terrain to make use of that. Incas had pulley systems, which indicates they could probably have built an axle quite easily too, but had no use for it, because, well, no flat roads.
And even then Northern Manchurians knew about the wheel for sure, and knew about roads, but still used sleds until at least the Russian conquest.
Sorry, I'm quite boring about this, but it bothers me when people talk about 'inventing the wheel' like it was something special. The wheel itself is meh. The axles are what makes it usable, and the roads make it useful.
Roads were also innvented everywhere. There were cultures with flat roads and no wagons. I would say the axle and then the spoked wheel were likely the big deals.
There's a ratio involving pi between the base lengths of the pyramid and its height. This is been interpreted by enthusiasts that the Egyptians knew about pi.
But, consider a measuring wheel, where you can mark off distances very accurately by counting revolutions of the wheel, say, 1 cubit in diameter (I know, I know, what's a cubit?). Then, if the height is laid out in cubits, the ratio of pi is there while being completely ignorant of it.