Measuring the height of the great pyramid with a stick

How could you measure height of the great pyramid in 6. century BC? How could Thales did? The answers are in the video.
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#thales #pyramid #height

[@blood635]

Carrion bro, this knowledge are helpful for us

[@TusharDeb]

Great video!

[@ekketomozin2810]

Very good video, but the name Thales is pronounced as two syllables, 'Tha' (rhymes with 'car') and '- les', (rhymes with 'keys').

[@jfcSharp]

Thanks. That was bugging me. I note other videos botch the 1st syllable.

[@ysadoraocumen329]

Thales is a genius.

[@user-zl8nh1bp6e]

I'm not sure that this method would yield a very accurate answer. You can only use the "half of the pyramid's base + length of the shadow" formula if the sun is exactly perpendicular to the side of the pyramid. That is, when half the side length corresponds to the distance from the midpoint of the pyramid's base to it's edge in the direction of the shadow. Otherwise it would be off. Wonder if Thales solved that somehow. (It would work well if the pyramid was conically shaped!)

[@ScienceWorld1]

According to Mathematic Magazine Vol73, No5, "During the spring and summer months, the shadow is also perpendicular to the west face once in the morning, and to the east face once in the afternoon." So Thales had twice change per day to do his calculation correctly.

[@user-zl8nh1bp6e]

@@ScienceWorld1 That's very interesting, thanks! I can't help wondering though, if Thales could solve the trig problem of the distance from the pyramid base's center to any point along the edge.

[@ScienceWorld1]

@@user-zl8nh1bp6e It will be a little imaginary but I think he could've. Let's say we measured the height of pyramid by using Thales method, also we know the length of the edges. So we can make a model of the pyramid. In order to determine coordinate of the point you talked about, we can use ratios. I mean, for example, if you choose a point on the one of the edge on the pyramid, we can measure how far that point to one of the corner, we know the ratio of the model, so we can determine where that point will be on the model. So there will be a triangle on the model. The triangle's corners consist of tip of the model, center of the base and your point. On the model, we know all distances (we can measure), on the pyramid we know the height. So model's height/pyramid's height = the distance from the model base's center to the point /the distance from the pyramid base's center to the point. We can calculate it without using any trigonometry equation.

[@Chararios]

Don't forget that the pyramids where built with "perfection" by the Egyptians.

[@programmer4047]

@@user-zl8nh1bp6e won't thales method always work as long as the triangle is isoceles or equilateral

[@shubhrajit2117]

At 2:24 half the length of the pyramid will work only when the Sun is symmetrical to the pyramid.

[@ScienceWorld1]

Yes you are right @Shubhrajit. In order to calculate the pyramid's height, Thales needed to wait for the moment when the shadow of the pyramid perpendicular to one of the sides. This happens once or twice on a day.

[@shubhrajit2117]

But now we have protractors to simplify the process:
brilliant.org/problems/bearing-the-giza/

[@moondigit007]

Using the method as illustrated by this video doesn't explain how Thales made the stick accurately parallel to the height line of the pyramid. He could have used 2 sticks, the first one twice the size of the second stick, and closer to the pyramid, and the second stick planted at the end of the shadow of the first one or he simply used a plumb line to plant the stick.Granted even though today we may perceive it as a crude
method of measuring, in principle Thales was correct.

[@babakopoulo]

Totally Mistake the video. He wasnt curius the height of Pyramid himself. Amasis Pharao and his Wise mathematicans and Engineers couldnt answrer to this. Thales visit Egypt and the asked him solve the problem. He said, i can colve it, it very easy...
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