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Doubling the cube is the construction, using only a straightedge and compass, of the edge of a cube that has twice the volume of a cube with a given edge. This is impossible because the cube root of 2, though algebraic, cannot be computed from integers by addition, subtraction, multiplication, division, and taking square roots.
Comparison of first and third-angle projections showing that related parts in the views are closer in third-angle. In first-angle projection, the object is conceptually located in quadrant I, i.e. it floats above and before the viewing planes, the planes are opaque, and each view is pushed through the object onto the plane furthest from it ...
A multiview projection is a type of orthographic projection that shows the object as it looks from the front, right, left, top, bottom, or back (e.g. the primary views), and is typically positioned relative to each other according to the rules of either first-angle or third-angle projection. The origin and vector direction of the projectors ...
Next, the cube is rotated ±45° about the vertical axis, followed by a rotation of approximately 35.264° (precisely arcsin 1 ⁄ √ 3 or arctan 1 ⁄ √ 2, which is related to the Magic angle) about the horizontal axis. Note that with the cube (see image) the perimeter of the resulting 2D drawing is a perfect regular hexagon: all the black ...
The left height gauge has the vernier scale, while the right one is an electronic height gauge with a digital readout. A height gauge is a measuring device used for determining the height of objects, and for marking of items to be worked on.
Rotary encoder for angle-measuring devices marked in 3-bit binary-reflected Gray code (BRGC). The inner ring corresponds to Contact 1 in the table. Black sectors are "on". Zero degrees is on the right-hand side, with angle increasing counter-clockwise. To avoid the above problem, Gray coding is used. This is a system of binary counting in which ...
A possible non-cube object that, viewed from appropriate angle, looks like an impossible cube. Impossible cube with forced perspective in Rotterdam, by Koos Verhoeff. The impossible cube draws upon the ambiguity present in a Necker cube illustration, in which a cube is drawn with its edges as line segments, and can be interpreted as being in either of two different three-dimensional orientations.
θ m is the angle between the space diagonal of a cube and any of its three connecting edges, see image. Another representation of the magic angle is half of the opening angle formed when a cube is rotated from its space diagonal axis, which may be represented as arccos − 1 / 3 or 2 arctan √ 2 radians ≈ 109.4712°.