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# opposite rays geometry example

From Wikipedia

Cross section (geometry)

In geometry, a cross-section is the intersection of a figure in 2-dimensional space with a line, or of a body in 3-dimensional space with a plane, etc. More plainly, when cutting an object into slices one gets many parallel cross-sections.

Cavalieri's principle states that solids with corresponding cross-sections of equal areas have equal volumes.

The cross-sectional area (A') of an object when viewed from a particular angle is the total area of the orthographic projection of the object from that angle. For example, a cylinder of height h and radius r has A' = \pi r^2 when viewed along its central axis, and A' = 2 \pi rh when viewed from an orthogonal direction. A sphere of radius r has A' = \pi r^2 when viewed from any angle. More generically, A' can be calculated by evaluating the following surface integral:

\,\! A' = \iint \limits_\mathrm{top} d\mathbf{A} \cdot \mathbf{\hat{r}},

where \mathbf{\hat{r}} is a unit vector pointing along the viewing direction toward the viewer, d\mathbf{A} is a surface element with outward-pointing normal, and the integral is taken only over the top-most surface, that part of the surface that is "visible" from the perspective of the viewer. For a convex body, each ray through the object from the viewer's perspective crosses just two surfaces. For such objects, the integral may be taken over the entire surface (A) by taking the absolute value of the integrand (so that the "top" and "bottom" of the object do not subtract away, as would be required by the Divergence Theorem applied to the constant vector field \mathbf{\hat{r}}) and dividing by two:

\,\! A' = \frac{1}{2} \iint \limits_A | d\mathbf{A} \cdot \mathbf{\hat{r}}|

Question:I need to know this for my geometry class. I take a regular geometry course and i need your help! Thanks

Answers:If guess if they are joined then a straight line

Question:It was a quetion that came up to me and a couple of friends.

Answers:You mean TWO OPPOSITE RAYS? like <------------> Hmm. That's pretty interesting. As we know Geometry, we can never state a statement if it has no proof, or there is no theorem/postulate that supports it. I can't recall a theorem in Euclidean Geometry that says: Two opposite rays determine a LINE. But yeah technically speaking, 2 opp. rays determine a line. But I'm no mathematician to claim it. :)

Question:Could you give me some ideas on how these examples of geometry terms are represented in real life? It is supposed to be objects. Here are the terms. Point Line Segment Ray Opposite Rays Perpendicular Lines Parrallel Lines Acute Angle Obtuse Angle Right Angle Vertical Angles (Acute only) Adjacent Angles (must be less than 180 Degrees) Linear Pair Thank you so much !

Answers:You have to put down tile or some type of flooring, you need to be able to use these to figure out how much tile to order and then how to lay this tile so that you have to cut the least amount (I mean really who wants to cut tiles for forever).

Question:A pair of adjacent angles whose noncommon sides are opposite rays