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| − | 3D Geometry deals with objects in 3 dimensions. For example, a drawing on a piece of paper is 2-dimensional since it has length and width. A baseball, on the other hand, is three-dimensional because it not only has length and width, but also depth.
| + | #REDIRECT [[3D Geometry]] |
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| − | == Making 3D Problems 2D ==
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| − | A very common technique for approaching 3D Geometry problems is to make it 2D. We can do this by looking at certain cross-sections of the diagram one at a time.
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| − | === Example ===
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| − | On a sphere with a radius of 2 units, the points <math> A </math> and <math> B </math> are 2 units away from each other. Compute the distance from the center of the sphere to the line segment <math> AB. </math>
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| − | ==== Solution ====
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| − | First, we note that the distance of a point to a line is usually meant to be the ''shortest'' distance between the point and the line. This occurs when the perpendicular to the line segment through the point is drawn.
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| − | Now that we know what we are looking for, we can choose an appropriate cross-section to look at. We choose to look at the cross-section containing <math> A, B </math> and the center of the sphere as shown in the following diagram:
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| − | <center>[[Image:sphere3d.PNG]]</center>
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| − | We now draw in the perpendicular to <math> AB </math>:
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| − | <center>[[Image:sphere3dtriangle.PNG]]</center>
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| − | From here, we can note the 30-60-90 triangle, or the Pythagorean Theorem, to find that <math> x = \sqrt{3} </math> units.
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| − | == See also ==
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| − | * [[Geometry]]
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| − | * [[Sphere]]
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| − | * [[Cylinder]]
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| − | * [[Cone]]
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| − | * [[Cube (geometry) | Cube]]
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| − | * [[Platonic solids]]
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| − | * [[Tetrahedron]]
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| − | * [[Octahedron]]
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| − | * [[Dodecahedron]]
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| − | * [[Icosahedron]]
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| − | Linked from 3D Geometry (https://artofproblemsolving.com/wiki/index.php/3D_Geometry)
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| − | {{stub}}
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