Geometric derivations of distance

In summary, Aristarchus was a Greek astronomer who first determined the distance between the Earth and the sun. He observed that when the moon was exactly half full, a right triangle was formed between the Earth (E), moon (M), and sun (S), with the right angle at the moon. He then used this information to calculate that the angle MES makes an angle of 87 degrees. The exact method he used to make this calculation is unknown, but it likely involved some form of astrolabe. Later, Edmond Halley also used Venus and parallax to determine the distance between Earth and the sun, but the exact method he used is not fully understood.
  • #1
adjkgh
23
0
aristarchus was the greek astronomer who was the first to find out the distance between the Earth and the sun. he observed that when the moon was exactly half full; the Earth (E), moon (M), and sun (S) formed a right triangle with the right angle at the moon.
then how did he found out that the angle MES makes an angle of 87 degrees? (also what was the distance from moon to Earth did he use?) give me derivations.
M-------------S
|_|
|
|
|
|
E


edmond halley used venus and parallax to find the distance between Earth and sun but i don't exactly understand how he did it. could someone please give me some derivations?

thanks.
 
Last edited:
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  • #2
I wasn't there at the time but I presume Aristarchus measured the angle with something like an Astrolabe.

By the way, since this doesn't seem to me to have anything to do with "Tensor Analysis & Differential Geometry" I am moving it to "General Mathematics"
 
  • #3
oh sorry. i wasnt exactly sure where it should be =/
 

1. What is a geometric derivation of distance?

A geometric derivation of distance is a mathematical process that uses geometric principles and formulas to calculate the distance between two points in a given space. It is often used in fields such as physics, engineering, and mathematics.

2. How is distance calculated using geometric derivations?

Distance is calculated using the Pythagorean theorem, which states that the square of the length of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides. In a geometric derivation, this formula is applied to the coordinates of the two points to determine their distance.

3. Can geometric derivations be used to calculate distance in any type of space?

Yes, geometric derivations can be used to calculate distance in any type of space, including two-dimensional, three-dimensional, and even higher dimensional spaces. As long as the coordinates of the two points are known, the distance can be determined using geometric principles.

4. Are there any limitations to using geometric derivations for distance calculations?

One limitation of using geometric derivations for distance calculations is that it assumes the space is Euclidean, meaning that it follows the rules of Euclidean geometry. If the space is non-Euclidean, such as in curved spaces, different formulas and principles must be used to calculate distance.

5. How are geometric derivations of distance used in real-world applications?

Geometric derivations of distance are used in various real-world applications, such as calculating the distance between two cities on a map, determining the distance between two points in a three-dimensional space for navigation, and measuring the distance between objects in physics experiments.

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