A square, a triangle, and a circle are the three fundamental forms. From these, all other forms are generated. The square is the basis of all flat objects: planes, sheets of paper, etc. The triangle is the basis of all three-dimensional objects: posts, balls, trees, etc.

The circle is the basis of **all round objects**: planets, stars, etc. It can be seen that flat objects are composed of squares and triangles, while round objects are composed of circles.

That's why artists usually start with simple shapes to get the effect they want. For example, if you wanted to paint a scene on a plane or sheet of paper, you would start by drawing some squares and triangles. Then add **some circles** to your painting to give it life and dimension.

As you can see, shapes play **an important role** in art. They help artists to create pictures that have direction, movement, and form. Knowing about **these shapes** will help you understand how paintings are created.

Circles, triangles, rectangles, rhombuses, squares, and trapezoids are the fundamental geometric plane forms. Many other figures can be constructed using **these elements**, but they all fall into one of the following categories: symmetrical or asymmetrical.

A symmetrical figure is one in which each part is identical to another part that is not visible. All polygons are symmetrical, as are many solids. Circles are the only polygon that is symmetrical in every dimension. Triangles are also symmetrical because if a triangle is rotated **either 180 degrees** or reflected across a vertical axis, it will appear the same as before. Similarly, squares and rectangles are symmetrical because if they are rotated or reflected, they will reappear in their original position.

Asymmetrical figures have parts that are not alike. They may have two similar but not exactly equal sides (such as two adjacent angles of a triangle). Or one side may be longer than the other (such as the base of a right triangle). Asymmetry can be found in most polygons, except circles and squares/rectangles. A circle has no inside or outside - only one center. So there's no way to say which part is larger than another.

Geometry has **numerous forms** dependent on **its measurements**. The 2-d forms are circles, triangles, squares, rectangles, kites, trapeziums, parallelograms, rhombuses, and other polygons. The fundamental three-dimensional forms are a cube, a cuboid, a sphere, a cone, and a cylinder. Geometric shapes are important in mathematics and physics.

Two dimensions: line, area. Three dimensions: volume. Four dimensions: time. Five dimensions: space-time. More than five dimensions: hyper-space.

Shape is a property of **some object or physical system**. A body can have more than one shape. Shapes can also change during the evolution of a system. For example, a crystal can be flat, thin, round, or irregular. However only solid objects can be shaped as desired without changing their identity. Liquid molecules are not fixed in place and can move around easily, which means that they cannot be shaped as desired.

In mathematics, a shape is any subset of **a metric space** (or ordered set). That is, a shape is a collection of points with a certain order and distance between them. Mathematical shapes include finite sets, infinite sets, and countably infinite sets.

A shape is called closed if it contains **its boundary**. That is, if you were to draw a picture of the set, then the set would be closed if the picture didn't show all of its sides.

Shapes can be divided into **two categories**: geometric and organic. Are easily identified, such as circles, squares, and triangles Such forms are frequently seen in architecture. In addition, geometric forms are used in the design of **many produced and handcrafted objects**. Organic forms are more complex and do not contain **identical parts** or elements. For example, plants are considered organic because they contain different amounts of water within their cells.

Geometric Shapes: These shapes are easily identifiable and often used in architecture as well as in other designs. They include circles, squares, and triangles.

Organic Shapes: These shapes are more complex and contain various amounts of water within their cells. Plants are an example of an organic shape. There are several other examples including shells, bones, leaves, and flowers.

Geometric shapes are made up of lines and angles. The most basic geometric figure is the circle. All circles are alike only if you ignore the fact that some are bigger than others. A small circle can be drawn with a pencil on a piece of paper. A large circle could be created by putting a bowl over **your head** and keeping it there for hours at a time!

The square is the fourth largest geometric figure after the circle, rectangle, and ellipse. It is made up of four equal sides and contains exactly one-quarter of a circle.

Oval, round, square, diamond, heart, pear, and oblong are the seven primary facial shapes. These general descriptions don't tell the whole story, but they can help identify **common patterns** among people.

The two main factors that determine a person's facial shape are genetics and posture. Genetics plays a role in any case where the features of two or more individuals are similar but not identical. For example, the father and son in this photo have the same genes, so they will tend to have similar features. However, because they are not identical, their appearances may vary somewhat from one another.

Posture also affects **facial shape**. People with prominent features tend to have individuals with prominent features as well. This is because those who are taller or broader at **the shoulder line** tend to have **longer faces**. They lack the support needed by parts of the skeleton to develop properly.

Individuals with **long faces** are often described as having "sloping" shoulders. This is because the upper arms are always seen as being longer than the lower arms, and the back of the neck tends to be flat or slightly angled forward.

Round faces are most common among males and females. The term "round face" actually describes an appearance rather than a specific shape.

Shapes are classified into two types: geometric and free-form. Geometric forms are exact shapes that can be expressed mathematically. Examples include squares, rectangles, and circles. Free-form shapes have no exact mathematical definition and cannot be expressed using only arithmetic operations. They include objects like teapots, chairs, and snowflakes.

Geometric shapes often serve as the basis for **more complex designs**. For example, a rectangle can be used as a foundation on which to build other structures such as windows or shelves. Free-form shapes are used to **their full potential** when incorporated into **design elements** such as patterns or colors. For example, a circle can be the center piece of a tablecloth or bowl while its surrounding lines make up the shape of the object.

People have used geometry since **ancient times**. It is believed that Egyptians invented some of the first tools used in geometry about 5,000 years ago. They made tools such as protractors and compass needles to measure and draw shapes.

In the West, mathematics became widely accepted after the work of Pythagoras (c. 570 B.C. - c. 500 B.C.) and Euclid (300 B.C. - 250 A.D.).