Daftar bentuk matematika

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Berikut ini adalah daftar dari beberapa bentuk matematis terdefinisi dengan baik .

Kurva aljabar sunting

Kurva rasional sunting

Derajat 2 sunting

Derajat 3 sunting

Derajat 4 sunting

Derajat 5 sunting

Kuintik l'Hospital^[1]

Derajat 6 sunting

Keluarga dengan derajat variabel sunting

Episikloid
Epispiral
Epitrokoid
Hiposikloid
Kurva Lissajous
Spiral Poinsot: Sebenarnya bukan spiral
Kurva biasa rasional
Kurva Rose

Kurva dari genus satu sunting

Kurva dengan genus lebih dari satu sunting

Keluarga kurva dengan genus variabel sunting

Lemniskat polinomial
Kurva Fermat
Spiral sinusoidal: Sebenarnya bukan spiral
Superelips
Permukaan Hurwitz

Kurva transendental sunting

Konstruksi sesepenggal sunting

Kurva yang dihasilkan oleh kurva lain sunting

Evolut
Glissette
Involut
Isoptik memuat Ortoptik
Caustic memuat Diakaustik dan Katakaustik
Konkoid
Kurva invers
Kurva pedal negatif
Kurva pedal
Kurva ruji
Kurva sejajar
Ortotomik
Roulette
Sisoid
Strofoid

Kurva ruang sunting

Permukaan dalam ruang 3 dimensi sunting

Minimal surfaces sunting

Non-orientable surfaces sunting

Kuadrik sunting

Permukaan bola semu sunting

Permukaan aljabar sunting

See the list of algebraic surfaces.

Cayley cubic
Barth sextic
Clebsch cubic
Monkey saddle (saddle-like surface for 3 legs.)
Torus
Dupin cyclide (inversion of a torus)
Payung Whitney

Permukaan lainnya sunting

Right conoid (a ruled surface)

Fraktal sunting

Fraktal acak sunting

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Cari sumber: "Daftar bentuk matematika" – berita · surat kabar · buku · cendekiawan · JSTOR

von Koch curve with random interval
von Koch curve with random orientation
Boundary of Brownian motion^{[butuh rujukan]}
2D polymer^{[butuh rujukan]}
Percolation front in 2D, Corrosion front in 2D^{[butuh rujukan]}
diffusion-limited aggregation
Random walk with no self-intersection^[8]
3D polymer^{[butuh rujukan]}
2D percolation cluster hull^{[butuh rujukan]}
2D percolation cluster
Brownian motion
Lichtenberg figure
Brownian motion
Percolation theory
Multiplicative cascade

Politop beraturan sunting

Berikut adalah tabel yang memperlihatkan ringkasan mengenai politop beraturan yang dihitung dengan dimensi.

Dimensi	Cembung	Takcembung	Teselasi cembung Euklides	Teselasi cembung hiperbolik	Teselasi takcembung hiperbolik	Teselasi Hiperbolik dengan sel takhingga dan/atau gambar verteks	Politop abstrak
1	1 ruas garis	0	1	0	0	0	1
2	∞ polygons	∞ star polygons	1	1	0	0	∞
3	5 Platonic solids	4 Kepler–Poinsot solids	3 tilings	∞	∞	∞	∞
4	6 convex polychora	10 Schläfli–Hess polychora	1 honeycomb	4	0	11	∞
5	3 convex 5-polytopes	0	3 tetracombs	5	4	2	∞
6	3 convex 6-polytopes	0	1 pentacombs	0	0	5	∞
7+	3	0	1	0	0	0	∞

There are no nonconvex Euclidean regular tessellations in any number of dimensions.

Polytope elements sunting

The elements of a polytope can be considered according to either their own dimensionality or how many dimensions "down" they are from the body.

Puncak, sebuah elemen dimensi 0
Sisi, sebuah elemen dimensi 1
Wajah, sebuah elemen dimensi 2
Sel, sebuah elemen dimensi 3
Hipersel, sebuah elemen dimensi 4
Facet, sebuah (n-1)
Ridge, sebuah elemen dimensi (n-2)
Peak, sebuah elemen dimensi (n-3)

For example, in a polyhedron (3-dimensional polytope), a face is a facet, an edge is a ridge, and a vertex is a peak.

Vertex figure: not itself an element of a polytope, but a diagram showing how the elements meet.

Teselasi sunting

The classical convex polytopes may be considered tessellations, or tilings, of spherical space. Tessellations of euclidean and hyperbolic space may also be considered regular polytopes. Note that an 'n'-dimensional polytope actually tessellates a space of one dimension less. For example, the (three-dimensional) platonic solids tessellate the 'two'-dimensional 'surface' of the sphere.

Dimensi nol sunting

Titik (geometri)

Politop regular satu dimensi sunting

Terdapat hanya satu politop dalam 1 dimensi, yang batasnya terdapat dua titik akhir ruas garis, diwakili oleh simbol Schläfli kosong {}.

Politop regular dua dimensi sunting

Cembung sunting

Merosot (bola) sunting

Takcembung sunting

Teselasi sunting

Apeirogon

Politop regular tiga dimensi sunting

Polihedron

Cembung sunting

Platonic solid
- Tetrahedron, the 3-space Simplex
- Cube, the 3-space hypercube
- Octahedron, the 3-space Cross-polytope
- Dodecahedron
- Icosahedron

Degenerate (spherical) sunting

Takcembung sunting

Kepler–Poinsot polyhedra

Tessellations sunting

Euclidean tilings sunting

Hyperbolic tilings sunting

Hyperbolic star-tilings sunting

Four-dimensional regular polytopes sunting

convex regular 4-polytope
- 5-cell, the 4-space Simplex
- 8-cell, the 4-space Hypercube
- 16-cell, the 4-space Cross-polytope
- 24-cell
- 120-cell
- 600-cell

Degenerate (spherical) sunting

Non-convex sunting

Star or (Schläfli–Hess) regular 4-polytope

Tessellations of Euclidean 3-space sunting

Degenerate tessellations of Euclidean 3-space sunting

Tessellations of hyperbolic 3-space sunting

Five-dimensional regular polytopes and higher sunting

Simplex	Hypercube	Cross-polytope
5-simplex	5-cube	5-orthoplex
6-simplex	6-cube	6-orthoplex
7-simplex	7-cube	7-orthoplex
8-simplex	8-cube	8-orthoplex
9-simplex	9-cube	9-orthoplex
10-simplex	10-cube	10-orthoplex
11-simplex	11-cube	11-orthoplex

Tessellations of Euclidean 4-space sunting

Tessellations of Euclidean 5-space and higher sunting

Tessellations of hyperbolic 4-space sunting

Tessellations of hyperbolic 5-space sunting

Apeirotopes sunting

Apeirotope

Abstract polytopes sunting

Abstract polytope
- 11-cell
- 57-cell

Non-regular polytopes sunting

Bagian ini kosong. Anda bisa membantu dengan melengkapinya. (November 2014)

2D with 1D surface sunting

Polygons named for their number of sides

Tilings sunting

Uniform polyhedra sunting

Regular polyhedron
- Platonic solid
- Kepler–Poinsot polyhedron (regular star polyhedra)
- Abstract regular polyhedra (Projective polyhedron)
Archimedean solid
Prismatic uniform polyhedron
- Prism
- Antiprism

Uniform star polyhedron

Duals of uniform polyhedra sunting

Catalan solid

non-convex

Johnson solids sunting

Other nonuniform polyhedra sunting

Spherical polyhedra sunting

Honeycombs sunting

Convex uniform honeycomb

Dual uniform honeycomb

Others

Convex uniform honeycombs in hyperbolic space

Other sunting

Regular and uniform compound polyhedra sunting

Polyhedral compound and Uniform polyhedron compound

Convex regular 4-polytope

5-cell, Tesseract, 16-cell, 24-cell, 120-cell, 600-cell

Abstract regular polytope

11-cell, 57-cell

Schläfli–Hess 4-polytope (Regular star 4-polytope)

Icosahedral 120-cell, Small stellated 120-cell, Great 120-cell, Grand 120-cell, Great stellated 120-cell, Grand stellated 120-cell, Great grand 120-cell, Great icosahedral 120-cell, Grand 600-cell, Great grand stellated 120-cell

Uniform 4-polytope

Prismatic uniform polychoron

Honeycombs sunting

5D with 4D surfaces sunting

regular 5-polytope
- 5-dimensional cross-polytope
- 5-dimensional hypercube
- 5-dimensional simplex

Five-dimensional space, 5-polytope and uniform 5-polytope

Prismatic uniform 5-polytope: For each polytope of dimension n, there is a prism of dimension n+1.^{[butuh rujukan]}

Honeycombs sunting

Six dimensions sunting

Seven dimensions sunting

Eight dimension sunting

Eight-dimensional space, uniform 8-polytope

Honeycombs sunting

Nine dimensions sunting

9-polytope

Hyperbolic honeycombs sunting

E₉ honeycomb

Ten dimensions sunting

10-polytope

Dimensional families sunting

Regular polytope and List of regular polytopes

Uniform polytope

Honeycombs

Geometri sunting

Segitiga
Automedian triangle
Delaunay triangulation
Segitiga sama sisi
Golden triangle
Hyperbolic triangle (non-Euclidean geometry)
Segitiga sama kaki
Segitiga Kepler
Segitiga Reuleaux
Segitiga siku-siku
Sierpinski triangle (fractal geometry)
Special right triangles
Spiral of Theodorus
Thomson cubic
Triangular bipyramid
Triangular prism
Triangular pyramid
Triangular tiling

Geometry and other areas of mathematics sunting

Glyphs and symbols sunting

Referensi sunting

^ "Courbe a Réaction Constante, Quintique De L'Hospital" [Kurva Reaksi Konstan, Quintic l'Hospital].
^ https://web.archive.org/web/20041114002246/http://www.mathcurve.com/courbes2d/isochron/isochrone%20leibniz. Diarsipkan dari versi asli tanggal 14 November 2004. Tidak memiliki atau tanpa |title= (bantuan)
^ https://web.archive.org/web/20041113201905/http://www.mathcurve.com/courbes2d/isochron/isochrone%20varignon. Diarsipkan dari versi asli tanggal 13 November 2004. Tidak memiliki atau tanpa |title= (bantuan)
^ Ferreol, Robert. "Spirale de Galilée". www.mathcurve.com.
^ Weisstein, Eric W. "Seiffert's Spherical Spiral". mathworld.wolfram.com.
^ Weisstein, Eric W. "Slinky". mathworld.wolfram.com.
^ "Monkeys tree fractal curve". Diarsipkan dari versi asli tanggal 21 September 2002.
^ WOLFRAM Demonstrations Project http://demonstrations.wolfram.com/SelfAvoidingRandomWalks/#more. Diakses tanggal 14 June 2019. Tidak memiliki atau tanpa |title= (bantuan)
^ Weisstein, Eric W. "Hedgehog". mathworld.wolfram.com.
^ "Courbe De Ribaucour" [Ribaucour curve]. mathworld.wolfram.com.

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