Geometric Shapes

Shape (OE. sceap Eng. created thing), refers to the external two-dimensional outline, appearance or configuration of some thing — in contrast to the matter or content or substance of which it is composed. more...

Home
Art
Basketry
Bead Art
Candle & Soap Making
Ceramics, Pottery
Crafts Wholesale Lots
Crocheting
Cross Stitch
Decorative, Tole Painting
Drawing
Embroidery
Fabric
Fabric Embellishments
Floral Crafts
Framing & Matting
General Art & Craft Supplies
Glass Art Crafts
Handcrafted Items
Kids Crafts
Knitting
Lacemaking, Tatting
Latch Rug Hooking
Leathercraft
Macramé
Metalworking
Mosaic
Needlepoint
Other Arts & Crafts
Painting
Paper Crafts & Origami
Quilting
Ribbon
Rubber Stamping & Embossing
Scrapbooking
Adhesives, Glue & Tape
Computerized, Digital
Cutters & Trimmers
Decoupage
Die Cutting Machines
Dies
Embellishments
Idea Books
Markers, Pens
Organizers & Carriers
Other Scrapbooking
Paper Piecing
Paper Punches
Animals & Insects
Borders, Corners
Collections, Mixed Lots
Flowers, Leaves
Geometric Shapes
Holidays & Occasions
Other Themes
Photo Mounting Paper
Scrapbook Patterns
Scrapbook Templates
Scrapbooking Albums
Scrapbooking Kits
Scrapbooking Paper, Pages
Scrapbooking Tools &...
Stickers
Sewing
Shellcraft
Spinning
Upholstery
Wall Décor, Tatouage
Weaving
Woodworking
Yarn

In geometry, traditionally two sets have the same shape if one can be transformed to another by a combination of translations, rotations (also called rigid transformations or congruency transformations) and uniform scalings. In other words, the shape of a set is all the geometrical information that is invariant to location (including rotation) and scale. Shapes of physical objects are equal if the subsets of space these objects occupy satisfy the definition above. In particular, the shape does not depend on the size of the object nor on changes in orientation/direction. However, a mirror image could be called a different shape. Shape may change if the object is scaled non uniformly. For example, a sphere becomes an ellipsoid when scaled differently in the vertical and horizontal direction. In other words, preserving axes of symmetry (if they exist) is important for preserving shapes. Also, shape is not necessary determined by only the outer boundary of an object. For example, a solid ice cube and a second ice cube containing an inner cavity (air bubble) do not necessarily have the same shape, even though the outer boundary is identical.

Objects that can be transformed into each other only by rigid transformations and mirroring are congruent. An object is therefore congruent to its mirror image (even if it is not symmetric), but not to a scaled version. Objects that have the same shape or one has the same shape as the other's mirror image (or both if they are themselves symmetric) are called geometrically similar. Thus congruent objects are always geometrically similar, but geometrical similarity additionally allows uniform scaling.

Simple shapes can be described by basic geometry such as points, line, curves, plane, and so on. Nevertheless, shapes we encounter in the real world are often quite complex (e.g. curved as studied by differential geometry, especially Riemannian geometry) or even fractal (showing the same pattern on different resolutions, e.g. plants or coastlines).

Shape can also be more loosely defined as "the appearance of something, especially its outline". This definition is consistent with the above, in that the shape of a set does not depend on its position, size or orientation. However, it does not always imply an exact mathematical transformation. For example it is common to talk of star-shaped objects even though the number of points of the star is not defined. A more flexible definition of shape takes into consideration the fact that we often deal with deformable shapes in reality (e.g. a person in different postures, a tree bending in the wind or a hand with different finger positions). By allowing also isometric (or near-isometric) deformations like bending, the intrinsic geometry of the object will stay the same, while subparts might be located at very different positions in space. This definition uses the fact, that geodesics (curves measured along the surface of the object) stay the same, independent of the isometric embedding. This means that the distance from a finger to a toe of a person measured along the body is always the same, no matter how the body is posed. An ant climbing a bendable plant will not notice how the wind moves it around, as only bending and no stretching is involved.

Read more at Wikipedia.org