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A drawing of a butterfly with bilateral symmetry, with left and right sides as mirror images of each other.. In geometry, an object has symmetry if there is an operation or transformation (such as translation, scaling, rotation or reflection) that maps the figure/object onto itself (i.e., the object has an invariance under the transform). [1]
The Pythagorean comma shown as the gap (on the right side) which causes a 12-pointed star to fail to close, which star represents the Pythagorean scale; each line representing a just perfect fifth. That gap has a central angle of 7.038 degrees, which is 23.46% of 30 degrees. The size of a Pythagorean comma, measured in cents, is
The type of symmetry is determined by the way the pieces are organized, or by the type of transformation: An object has reflectional symmetry (line or mirror symmetry) if there is a line (or in 3D a plane) going through it which divides it into two pieces that are mirror images of each other. [6]
It said "Although authorities on punctuation may differ, when drafting Maine law or rules, don't use a comma between the penultimate and the last item of a series." [ 60 ] In addition to the absence of a comma, the fact that the word chosen was "distribution" rather than "distributing" was also a consideration, [ 61 ] as was the question of ...
In English writing, quotation marks or inverted commas, also known informally as quotes, talking marks, [1] [2] speech marks, [3] quote marks, quotemarks or speechmarks, are punctuation marks placed on either side of a word or phrase in order to identify it as a quotation, direct speech or a literal title or name.
Suppose that, for three circles α, β, and γ, there is a circle of antisimilitude for the pair (α,β) that crosses a second circle of antisimilitude for the pair (β,γ). Then there is a third circle of antisimilitude for the third pair (α,γ) such that the three circles of antisimilitude cross each other in two triple intersection points ...
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.
Not every parallelogram is a rhombus, though any parallelogram with perpendicular diagonals (the second property) is a rhombus. In general, any quadrilateral with perpendicular diagonals, one of which is a line of symmetry, is a kite. Every rhombus is a kite, and any quadrilateral that is both a kite and parallelogram is a rhombus.