If one looks at a glass cube straight on so it resembless a 2-d square of 1 x1,what would the measurement of?

Question

the square of the square oppisite apear to be? the cube being looked directly at will resemble a flat square and the other side would also resemble a flat square in the center of the first flat square.How mathematically is the second square's appearance of smaller size ,due to perspective, calculated? This also can be asked differently: if one has two flat squares1x1 in size, what would the relation of the second to first one be if it was held 1 distance behind the first ?.The moon appears to be small because of distance, what is used to determine or calculate how distance effects the appearance of an object's size?

Answer 1

Clearly, this depends on how far away you are from the cube. This is much easier to visualize with a picture, so I will try to describe one:

Start with square ABCD. Assume you are at point E at distance n from the square, with AB being the side of the square closest to you. Let points F and G be the midpoints of opposite sides AB and CD of the square.

Now draw the line connecting points E, F, and G. Note the length of line segment EF is n, while the length of line segment FG is 1. Also, the length of line segments FB and GC are both 1/2.

Now draw lines EB and CD (i.e. extend the back side of the square) until the two lines intersect at point H. You can calculate the length of line segment GH using similar triangles:

GH/EG = FB/EF. Plugging some numbers in gives you:

GH/(n+1) = 0.5/n

GH = (n+1)/2n.

OK, after all that work, let's get back to your question. You are asking: how much bigger does the closer square appear? Note that, for the two squares to appear to be the same size, the back side would have to be the length of GH. Therefore, the amount that the back side appears to shrink is actually GC/GH. The rest is just algebra:

GC/GH =

1/2 / (n+1)/2n, which simplifies to n/(n+1).

For example, if you are 10 units away from a square of 1 unit, the back side of the square appears to be 10/11 the size of the front side.

Answer 2

I'm not going to explain all that specifically, but the moon's size is calculated on something called angular distance. You use the same concept as the two squares one behind the other.

You put a known object between you and the moon so that your perspective lines up the two sides exactly with the two sides of the moon. You then use the angle between your eye and the sides of the moon and the sides of the known object as a triangular reference. you put the size of the object in to get the angle, but you need to know the distance the moon is from the earth. you use that as the altitude of the triangle, the moon's unknown width as the base, and you calculate using isosceles geometry. To find the exact angle, you need a sextant. Then you do the math, which I can't remember at the moment.

Answer 3

Q- Why does the moon appear to be small.
A- Because ...the moom is small
Mystery solved it's like less than 1/80 the size of earth that's why it has lower gravity, no atmosphere, etc,

I know what your talking about also I have no idea how the math goes though.