NEW DEMO

Here is a brief description of geometry.

Geometry is a branch of mathematics that deals with the measurement, properties, and relationships of points, lines, angles, surfaces, and solids. It is concerned with the study of space, including the distance, shape, size, and relative position of figures.

Geometry encompasses both plane geometry, which focuses on two-dimensional shapes such as triangles, squares, and circles, and solid geometry, which deals with three-dimensional shapes like cubes, spheres, and cones.

The fundamental concepts of geometry include:

• Points: precise locations or places on a plane or in space.
• Lines sets of points extending infinitely in two directions.
• Angles: formed by the intersection of two lines or planes.
• Planes: flat surfaces extending infinitely in all directions.
• Solid: three-dimensional objects with volume and surface area.
• Curve: A curve in geometry is a set of points that satisfy a specific mathematical relationship, typically defined by an equation or a function. In essence, a curve is a continuous, smooth, and non-self-intersecting path in space, often visualized as a line that bends or curves.

Geometry has numerous applications in various fields, including:

• Architecture and engineering
• Art and design
• Physics and astronomy
• Computer science and graphics
• Navigation and cartography

In essence, geometry is the study of the properties and relationships of shapes and spaces, providing a framework for understanding and describing the world around us. (Most of thi description was obtained as an AL search in browser BRAVE for "What is geometry.)

We are going to focus on a type of curve (notice the long description) together with art and design plus the inherent mathematics. The curves are spirals.

Here is a sample of spirals in the figure below.

To see more images click on any of the following: Geometric Spiral Images or Twisted math and beautiful geometry. Of course you can find many other spiral image collections. For a history of geometry, main concepts, and applications click here Wikipedia geometry.

We have a demo that focuses on classical spirals using polar coordinates, graphs, and curves click here Spirals in MATHDEMOS.org.

David R. Hill: To see our collection of demos click on Demos for instructors and/or students.