Formes geomètriques
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The document covers geometric shapes, categorizing polygons and polyhedra, along with their properties and classifications. It explains the naming conventions for polygons based on the number of sides, introduces regular and irregular polygons, and discusses various types of polyhedra including Platonic and Archimedean solids. Key geometric concepts such as vertices, edges, and angles are also detailed throughout.
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Formes geomètriques
- 1. UNITAT 1: FORMES GEOMÈTRIQUES GEOMETRIC SHAPES EDUCACIÓ VISUAL I PLÀSTICA – 1 ESO Escola Betúlia - 2014 -2015
- 3. Polígon - Polygon Side or edges The segments are called sides or edges The edges where two segments meet are the polygon’s vertices (sing vertex) or corners vertex Cambridge definition: a flat shape with three or more straight sides
- 4. Polygon
- 5. You can make names using this method: ...end with+1 ...henagon+2 ...digon+3 ...trigon+4 ...tetragon+5 ...pentagon+6 ...hexagon+7 ...heptagon+8 ...octagon+9 Start with... 20 Icosi... 30 Triaconta... 40 Tetraconta... 50 Pentaconta... 60 Hexaconta... 70 Heptaconta... 80 Octaconta... 90 Enneaconta... 100 Hecta... etc.. Example: a 63-sided polygon is a Hexacontadigon BUT, for polygons with 13 or more sides, it is OK (and easier) to write "13-gon", "14-gon" ... "100-gon", etc.
- 7. Triangle A plane figure with three straight sides and three angles A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. Equilateral Isosceles Scalene
- 8. Quadrilateral A quadrilateral is a polygon with four sides (or edges) and four vertices or corners. Simple quadrilateral Complex quadrilateral
- 9. Quadrilateral The interior angles of a simple (and planar) quadrilateral ABCD add up to 360 degrees of arc, that is
- 10. Pentagon A pentagon is any five-sided polygon. A pentagon may be simple or self- intersecting. The sum of the internal angles in a simple pentagon is 540°. A pentagram is an example of a self-intersecting pentagon. A regular pentagon, all sides are equal in length and each interior angle is 108°
- 11. Polyhedron A polyhedron (plural polyhedra or polyhedrons) is a solid in three dimensions with flat faces, straight edges and sharp corners or vertices (singular: vertex). face edge Corner or vertex
- 12. Regular Polyhedron Tetrahedron Hexahedron Octahedron Dodecahedron Icosahedron 3 faces 4 faces 8 faces 12 faces 20 faces Known as the Platonic solids
- 13. Regular Polyhedron Small stellated dodecahedron Great dodecahedron Great stellated dodecahedron Great icosahedron 12 pentagrammic faces 12 pentagonal faces 12 intersecting pentagrammic faces 20 intersecting triangular faces Known as the Kepler-Poinsot polyhedra
- 14. Pentagons in polyhedra Dodecahedron Pyritohedron Pentagonal icositetrahedron Pentagonal hexecontahedron Truncated_ trapezohedron
- 15. Archimedean solid An Archimedean solid is a highly symmetric, semi-regular convex polyhedron composed of two or more types of regular polygons meeting in identical vertices Truncated tetrahedron Cuboctahedron Truncated hexahedron Truncated octahedron Small rhombicuboctahedron Great rhombicuboctahedron Snub hexahedron Icosidodecahedron Truncated dodecahedron Truncated icosahedron 4 triangles 4 hexagons 8 triangles 6 squares 8 triangles 6 octagons 6 squares 8 hexagons 8 triangles 18 squares 12 squares 8 hexagons 6 octagons 32 triangles 6 squares 20 triangles 12 pentagons 20 triangles 12 decagons 12 pentagons 20 hexagons
- 16. Archimedean solid Small rhombicosidodecahedron Great rhombicosidodecahedron Snub dodecahedron 20 triangles 30 squares 12 pentagons 30 squares 20 hexagons 12 decagons 8 triangles 6 octagons
Editor's Notes
- #4: En geometría, un polígono es una figura plana compuesta por una secuencia finita desegmentos rectos consecutivos que cierran una región en el plano. Estos segmentos son llamados lados, y los puntos en que se intersecan se llaman vértices. El interior del polígono es llamado área. El polígono es el caso bidimensional del politopo, figura geométrica general definida para cualquier número de dimensiones. A su vez, un politopo de tres dimensiones se denomina poliedro, y de cuatro dimensiones se denomina polícoro. La palabra polígono deriva del griego antiguo πολύγωνος (polúgonos), a su vez formado por πολύ (polú) ‘muchos’ y γωνία (gōnía) ‘ángulo’,1 2 3 aunque hoy en día los polígonos son usualmente entendidos por el número de sus lados. In geometry a polygon /ˈpɒlɪɡɒn/ is traditionally a plane figure that is bounded by a finite chain of straight line segments closing in a loop to form a closed chain or circuit. These segments are called its edges or sides, and the points where two edges meet are the polygon's vertices (singular: vertex) or corners. The interior of the polygon is sometimes called its body. An n-gon is a polygon with n sides. A polygon is a 2-dimensional example of the more general polytope in any number of dimensions. The word "polygon" derives from the Greek πολύς (polús) "much", "many" and γωνία (gōnía) "corner", "angle", or γόνυ (gónu) "knee".[1]
- #5: Triangle (or Trigon)360° Quadrilateral (or Tetragon)490° Pentagon5108° Hexagon6120° Heptagon (or Septagon)7128,571° Octagon8135° Nonagon (or Enneagon)9140° Decagon10144° Hendecagon (or Undecagon)11147,273° Dodecagon12150° Triskaidecagon13 152,308° Tetrakaidecagon14 154,286° Pentadecagon15 156° Hexakaidecagon16 157,5° Heptadecagon17 158,824° Octakaidecagon18 160° Enneadecagon19 161,053° Icosagon20 162° Triacontagon30 168° Tetracontagon40 171° Pentacontagon50 172,8° Hexacontagon60 174° Heptacontagon70 174,857° Octacontagon80 175,5° Enneacontagon90 176° Hectagon100 176,4° Chiliagon1.000 179,64° Myriagon10.000 179,964° Megagon1.000.000 ~180°Googolgon10100 ~180°n-gonn(n-2) × 180° / n
- #9: In geometry, a square is a regular quadrilateral, which means that it has four equal sides and four equal angles (90-degree angles, or right angles)
- #17: You can make names using this method: Sides Start with...20 Icosi...30 Triaconta...40 Tetraconta...50 Pentaconta...60 Hexaconta...70 Heptaconta...80 Octaconta...90 Enneaconta...100 Hecta...etc.. Sides ...end with+1 ...henagon+2 ...digon+3 ...trigon+4 ...tetragon+5 ...pentagon+6 ...hexagon+7 ...heptagon+8 ...octagon+9 ...enneagonExample: a 62-sided polygon is a Hexacontadigon