Geometry: Overview, Branches, Formulas, Angles

It’s like a puzzle where you figure out how things fit, how big or small they are, and how they can move. Through geometry, kids develop important skills in problem-solving, creativity, and critical thinking while exploring the world of shapes in fun and exciting ways.

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Branches of Geometry

The branches of geometry are categorized as:

• Algebraic geometry
• Discrete geometry
• Differential geometry
• Euclidean geometry
• Convex geometry
• Topology

Algebraic Geometry

This area of geometry focusses on the multivariate polynomial's zeros. It contains algebraic equations for solving sets of zeros, both linear and polynomial. Applications of this kind include string theory, cryptography, and more.

Discrete Geometry

It is concerned with the relative position of simple geometric objects, such as points, lines, triangles, circles etc.

Differential Geometry

It solves problems by applying algebraic and calculus methods. General relativity in physics is one of the many issues.

Euclidean Geometry

Axioms and theorems pertaining to points, lines, planes, angles, congruence, similarity, and solid figures are used in the study of plane and solid figures. It has several uses in computer science, solving problems in modern mathematics,

Convex Geometry

Using real analytic techniques, it incorporates convex shapes in Euclidean space. It can be used in number theory for functional analysis and optimisation.

Topology

The characteristics of space under continuous mapping are its focus. Compactness, completeness, continuity, filters, function spaces, grills, clusters and bunches, hyperspace topologies, initial and final structures, metric spaces, nets, proximal continuity, proximity spaces, separation axioms, and uniform spaces are some of the factors that are taken into account in its use.

Angles

Geometry Formulas

Geometry formulae are essential for calculating the area, perimeter, volume, and other measurements utilising the length, width, and height of various geometrical forms. We may easily calculate the measures by utilising the formulas. In geometry, there are a tonne of formulas to memorise.

Plane Geometry (Two-dimensional Geometry)

Flat shapes that can be sketched on paper are the subject of plane geometry. These consist of two-dimensional triangles, circles, and lines. Two-dimensional geometry is another name for plane geometry. There are only two measurements for each two-dimensional figure, such as length and width. It doesn't address the forms' depth. The square, triangle, rectangle, circle, and so on are a few types of plane figures. The important terminologies in plane geometry are:

• Point
• Line
• Angles

Point

On a plane, a point is a specific location. They are typically represented by a dot. It is crucial to recognise that a point is a location rather than an object. Additionally, keep in mind that a point has no dimensions; ideally, it has only one position.

Line

The line has no thickness, is straight (no curves), and stretches in both directions indefinitely. It is crucial to remember that a line is created by joining infinite points. In geometry, the x-axis is a horizontal line, while the y-axis is a vertical line.

Natural Numbers

Angles in Geometry

An angle in planar geometry is the shape created by two rays, known as the angle's sides, that share a common termination, known as the angle's vertex.

Types of Angle

Acute Angle – An Acute angle (or Sharp angle) is an angle smaller than a right angle ie. it can range between 0 – 90 degrees.

Obtuse Angle – An Obtuse angle is more than 90 degrees but is less than 180 degrees.

Right Angle – An angle of 90 degrees.

Straight Angle – An angle of 180 degrees is a straight angle, i.e. the angle formed by a straight line

Circle in Geometry

One basic closed shape is a circle. All of a circle's points are the same constant distance from a point known as the centre; that is, the curve drawn by a moving point whose distance from the centre is constant.

Solid Geometry (Three-dimensional Geometry)

Three-dimensional objects such as cubes, prisms, cylinders, and spheres are the subject of solid geometry. It addresses the figure's three dimensions, including height, width, and length. However, some solids—like spheres—do not have faces. The study of three dimensions in Euclidean space is known as solid geometry. We are surrounded by three-dimensional objects. The rotation operation of 2D objects yields all three-dimensional shapes. The following are crucial characteristics of 3D shapes:

• Faces
• Edges
• Vertices

Go through these terms in detail for different geometric shapes here.