Calculate with the intercept theorem to set the height and shadow length of two objects in relation. The intercept theorem states, among other things, that the ratio of height and length of the shadow cast by different objects standing next to each other is the same. So if you know three of the values, you can calculate the fourth.
Please enter three values, the fourth value will be calculated. Ratio height 1 / length 1 = height 2 / length 2
Example: Thales of Miletus used the intercept theorem to determine the height of the Great Pyramid of Giza. He stuck a stick 1.63 meters high (the exact historical values are not known) into the ground and measured a shadow length of 2 meters. The shadow of the pyramid, from the top projected on the ground to the top of the shadow, was 180 meters long at the same time on the same day. Therefore, the height of the pyramid at that time was 146.7 meters. Due to erosion, the pyramid is now only 139 meters high.
Thales was one of the first known ancient Greek mathematicians and philosophers, he lived in the 7th and 6th century BC. The intercept theorem is also known as Thales' theorem. Thales a However, it was already known to the ancient Babylonians and Egyptians. The first known proof appears in Euclid's Elements, a good 250 years after Thales. The theorem states as follows: if two straight lines radiate from a point and are intersected by two parallel lines, then:
- the two resulting distances on one line are related to each other as those on the other line, and
- the intercepts of the two parallel lines are related to each other as the two intercepts of each of the straight lines.
The straight line segments can be considered as lengths, and the parallel segments can be considered as heights.
