Free, interactive video lessons on geometry! The mathematics of lines, shapes, and angles. Essential stuff for describing the world around you. Geometry Dash is a series of five video games developed by Sweden-based developer Robert Topala, and published by his company, RobTop Games. The principal game, Geometry Dash, it is a rhythm-based platforming game which currently has 21 official levels and has more than 40 million online levels made by players.
Geometry is all about shapes and their properties.
If you like playing with objects, or like drawing, then geometry is for you!
Geometry can be divided into:
Plane Geometry is about flat shapes like lines, circles and triangles ... shapes that can be drawn on a piece of paper
Solid Geometry is about three dimensional objects like cubes, prisms, cylinders and spheres.
| Hint: Try drawing some of the shapes and angles as you learn ... it helps. |
Point, Line, Plane and Solid
A Point has no dimensions, only position
A Line is one-dimensional
A Plane is two dimensional (2D)
A Solid is three-dimensional (3D)
Why?
Why do we do Geometry? To discover patterns, find areas, volumes, lengths and angles, and better understand the world around us.
Plane Geometry
Plane Geometry is all about shapes on a flat surface (like on an endless piece of paper).
- Rectangle, Rhombus, Square, Parallelogram, Trapezoid and Kite
- Square Calculator and Rectangle Calculator
Polygons
A Polygon is a 2-dimensional shape made of straight lines. Triangles and Rectangles are polygons.
Here are some more:
| Pentagon |
| Hexagon |
The Circle
Circle Theorems (Advanced Topic)
Symbols
There are many special symbols used in Geometry. Here is a short reference for you:
Congruent and Similar
Angles
Types of Angles
| Acute Angles | Right Angles | Obtuse Angles | Straight Angle | Reflex Angles | Full Rotation |
Using Drafting Tools |
Transformations and Symmetry
Transformations:
- Rotation
- Reflection
- Translation
Symmetry:
Coordinates
More Advanced Topics in Plane Geometry
Pythagoras
Conic Sections
Circle Theorems
Trigonometry
Trigonometry is a special subject of its own, so you might like to visit:
Solid Geometry
Solid Geometry is the geometry of three-dimensional space - the kind of space we live in ...
... let us start with some of the simplest shapes:
Polyhedra and Non-Polyhedra
There are two main types of solids, 'Polyhedra', and 'Non-Polyhedra':
Polyhedra(they must have flat faces):
| Cubes and Cuboids (Volume of a Cuboid) |
| Platonic Solids |
| Prisms |
| Pyramids |
Non-Polyhedra(when any surface is not flat):
| Sphere | Torus |
| Cylinder | Cone |
Geometry is the study of figures in a space of a given number of dimensions and of a given type. The most common types of geometry are plane geometry (dealing with objects like the point, line, circle, triangle, and polygon), solid geometry (dealing with objects like the line, sphere, and polyhedron), and spherical geometry (dealing with objects like the spherical triangle and spherical polygon). Geometry was part of the quadrivium taught in medieval universities.
A mathematical pun notes that without geometry, life is pointless. An old children's joke asks, 'What does an acorn say when it grows up?' and answers, 'Geometry' ('gee, I'm a tree').
Historically, the study of geometry proceeds from a small number of accepted truths (axioms or postulates), then builds up true statements using a systematic and rigorous step-by-step proof. However, there is much more to geometry than this relatively dry textbook approach, as evidenced by some of the beautiful and unexpected results of projective geometry (not to mention Schubert's powerful but questionable enumerative geometry).
The late mathematician E. T. Bell has described geometry as follows (Coxeter and Greitzer 1967, p. 1): 'With a literature much vaster than those of algebra and arithmetic combined, and at least as extensive as that of analysis, geometry is a richer treasure house of more interesting and half-forgotten things, which a hurried generation has no leisure to enjoy, than any other division of mathematics.' While the literature of algebra, arithmetic, and analysis has grown extensively since Bell's day, the remainder of his commentary holds even more so today.
Formally, a geometry is defined as a complete locally homogeneous Riemannian manifold. In , the possible geometries are Euclidean planar, hyperbolic planar, and elliptic planar. In , the possible geometries include Euclidean, hyperbolic, and elliptic, but also include five other types.
SEE ALSO:Absolute Geometry, Affine Geometry, Analytic Geometry, Cartesian Coordinates, Combinatorial Geometry, Computational Geometry, Differential Geometry, Discrete Geometry, Enumerative Geometry, Finsler Geometry, Inversive Geometry, Kawaguchi Geometry, Nil Geometry, Non-Euclidean Geometry, Ordered Geometry, Plane Geometry, Projective Geometry, Sol Geometry, Solid Geometry, Spherical Geometry, Stochastic Geometry, Thurston's Geometrization ConjectureREFERENCES:
Altshiller-Court, N. College Geometry: A Second Course in Plane Geometry for Colleges and Normal Schools, 2nd ed., rev. enl. New York: Barnes and Noble, 1952.
Bogomolny, A. 'Geometry.' https://www.cut-the-knot.org/geometry.shtml.
Bold, B. FamousProblems of Geometry and How to Solve Them. New York: Dover, 1964.
Cinderella, Inc. 'Cinderella: The Interactive Geometry Software.' https://www.cinderella.de/.
Coxeter, H. S. M. Introductionto Geometry, 2nd ed. New York: Wiley, 1969.
Coxeter, H. S. M. TheBeauty of Geometry: Twelve Essays. New York: Dover, 1999.
Coxeter, H. S. M. and Greitzer, S. L. GeometryRevisited. Washington, DC: Math. Assoc. Amer., 1967.
Croft, H. T.; Falconer, K. J.; and Guy, R. K. UnsolvedProblems in Geometry. New York: Springer-Verlag, 1994.
Davis, C.; Grünbaum, B.; and Scherk, F. A. TheGeometric Vein: The Coxeter Festschrift. New York: Springer, 1981.
Eppstein, D. 'Geometry Junkyard.' https://www.ics.uci.edu/~eppstein/junkyard/.
Eppstein, D. 'Many-Dimensional Geometry.' https://www.ics.uci.edu/~eppstein/junkyard/highdim.html.
Eppstein, D. 'Planar Geometry.' https://www.ics.uci.edu/~eppstein/junkyard/2d.html.
Eppstein, D. 'Three-Dimensional Geometry.' https://www.ics.uci.edu/~eppstein/junkyard/3d.html.
Eves, H. W. ASurvey of Geometry, rev. ed. Boston, MA: Allyn and Bacon, 1972.
Geometry Center. https://www.geom.umn.edu.
Ghyka, M. C. TheGeometry of Art and Life, 2nd ed. New York: Dover, 1977.
Hilbert, D. The Foundations of Geometry, 2nd ed. Chicago, IL: The Open Court Publishing Co., 1921.
Ivins, W. M. Artand Geometry. New York: Dover, 1964.
Johnson, R. A. Modern Geometry: An Elementary Treatise on the Geometry of the Triangle and the Circle. Boston, MA: Houghton Mifflin, 1929.
King, J. and Schattschneider, D. (Eds.). Geometry Turned On: Dynamic Software in Learning, Teaching and Research. Washington, DC: Math. Assoc. Amer., 1997.
Klee, V. 'Some Unsolved Problems in Plane Geometry.' Math. Mag.52,131-145, 1979.
Klein, F. FamousProblems of Elementary Geometry and Other Monographs. New York: Dover, 1956.
MathPages. 'Geometry.' https://www.mathpages.com/home/igeometr.htm.
Melzak, Z. A. Invitationto Geometry. New York: Wiley, 1983.
Meschkowski, H. Unsolvedand Unsolvable Problems in Geometry. London: Oliver & Boyd, 1966.
Moise, E. E. Elementary Geometry from an Advanced Standpoint, 3rd ed. Reading, MA: Addison-Wesley, 1990.
Ogilvy, C. S. 'Some Unsolved Problems of Modern Geometry.' Ch. 11 in Excursions in Geometry. New York: Dover, pp. 143-153, 1990.
Playfair, J. Elements of Geometry: Containing the First Six Books of Euclid, with a Supplement on the Circle and the Geometry of Solids to which are added Elements of Plane and Spherical Trigonometry. New York: W. E. Dean, 1861.
Simon, M. Über die Entwicklung der Elementargeometrie im XIX. Jahrhundert.Leipzig: Teubner, pp. 97-105, 1906.
Townsend, R. Chapters on the Modern Geometry of the Point, Line, and Circle, Being the Substance of Lectures Delivered in the University of Dublin to the Candidates for Honors of the First Year in Arts, 2 vols. Dublin: Hodges, Smith and Co., 1863.
Uspenskii, V. A. SomeApplications of Mechanics to Mathematics. New York: Blaisdell, 1961.
Geometry Dash Meltdown
Weisstein, E. W. 'Books about Geometry.' https://www.ericweisstein.com/encyclopedias/books/Geometry.html.
Woods, F. S. Higher Geometry: An Introduction to Advanced Methods in Analytic Geometry. New York: Dover, 1961.
Geometry Dash Online
Referenced on Wolfram|Alpha: GeometryCITE THIS AS:Geometry Dash Subzero
Weisstein, Eric W. 'Geometry.' From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Geometry.html