Search results
Results from the WOW.Com Content Network
The longest diagonals of a regular hexagon, connecting diametrically opposite vertices, are twice the length of one side. From this it can be seen that a triangle with a vertex at the center of the regular hexagon and sharing one side with the hexagon is equilateral, and that the regular hexagon can be partitioned into six equilateral triangles.
Comparison of sizes of regular polygons with the same edge length, from three to sixty sides. The size increases without bound as the number of sides approaches infinity. Of all n-gons with a given perimeter, the one with the largest area is regular. [10]
The honeycomb conjecture states that hexagonal tiling is the best way to divide a surface into regions of equal area with the least total perimeter. The optimal three-dimensional structure for making honeycomb (or rather, soap bubbles) was investigated by Lord Kelvin , who believed that the Kelvin structure (or body-centered cubic lattice) is ...
Brianchon's theorem can be proved by the idea of radical axis or reciprocation. To prove it take an arbitrary length (MN) and carry it on the tangents starting from the contact points: PL = RJ = QH = MN etc. Draw circles a, b, c tangent to opposite sides of the hexagon at the created points (H,W), (J,V) and (L,Y) respectively.
However, the theorem remains valid in the Euclidean plane, with the correct interpretation of what happens when some opposite sides of the hexagon are parallel. If exactly one pair of opposite sides of the hexagon are parallel, then the conclusion of the theorem is that the "Pascal line" determined by the two points of intersection is parallel ...
In mathematics, a symmetry operation is a geometric transformation of an object that leaves the object looking the same after it has been carried out. For example, a 1 ⁄ 3 turn rotation of a regular triangle about its center, a reflection of a square across its diagonal, a translation of the Euclidean plane, or a point reflection of a sphere through its center are all symmetry operations.
In geometry, a golden rectangle is a rectangle with side lengths in golden ratio +:, or :, with approximately equal to 1.618 or 89/55. Golden rectangles exhibit a special form of self-similarity : if a square is added to the long side, or removed from the short side, the result is a golden rectangle as well.
The chamfered cube is constructed as a chamfer of a cube: the squares are reduced in size and new faces, hexagons, are added in place of all the original edges. The cC is a convex polyhedron with 32 vertices, 48 edges, and 18 faces: 6 congruent (and regular) squares, and 12 congruent flattened hexagons.