Difference between revisions of "3D"

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3-D, or 3D, typically refers to something with three spatial dimensions, e.g., a cube. It is the term for an object with length, width, and height.
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#REDIRECT [[3D Geometry]]
 
 
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.
 
Contents
 
 
 
    1 Making 3D Problems 2D
 
        1.1 Example
 
            1.1.1 Solution
 
    2 See also
 
 
 
Making 3D Problems 2D
 
 
 
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.
 
Example
 
 
 
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>
 
Solution
 
 
 
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.
 
 
 
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:
 
Sphere3d.PNG
 
 
 
We now draw in the perpendicular to <math>AB</math>:
 
Sphere3dtriangle.PNG
 
 
 
From here, we can note the 30-60-90 triangle, or the Pythagorean Theorem, to find that <math>x = \sqrt{3}</math> units.
 
See also
 
 
 
    Geometry
 
    Sphere
 
    Cylinder
 
    Cone
 
    Cube
 
    Platonic solids
 
    Tetrahedron
 
    Octahedron
 
    Dodecahedron
 
    Icosahedron
 
    Rhombic dodecahedron
 

Latest revision as of 20:01, 16 January 2025

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