Theorems on Straight Lines and Plane In mathematics, the term “line” actually refers to the “straight line”. It is a one-dimensional figure that extends in two opposite directions. A straight line can be defined as an interconnected set of an infinite number of points. The length of a lin.....
Axioms: Solid Geometry Axioms involving reflection at a plane were approached through physical observations of reflection from a plane mirror. Axioms are general statements made about real numbers. Sometimes they are called algebraic postulates. Often what they say about real numbers holds true f.....
The dihedral angle is an angle between two distinct planes that are intersecting in any way. We can say that the interior angle between two planes is known as a dihedral angle. The plane angle between two intersecting planes is called a dihedral angle between the planes. It is an angle is the ang.....
Angle between a Straight Line and a Plane: In mathematics, the term “line” actually refers to the “straight line”. It is a one-dimensional figure that extends in two opposite directions. A straight line can be defined as an interconnected set of an infinite number of point.....
Orthogonal Projection: A projection of a figure by parallel rays. In such a projection, tangencies are preserved. Parallel lines project to parallel lines. The ratio of lengths of parallel segments is preserved, as is the ratio of areas. Orthogonal Projection is a system of making engineering dra.....
Angle between Two Skew Lines Skew Lines mean two or more lines which have no intersections but are not parallel, also called agonic lines. Since two lines in the plane must intersect or be parallel, skew lines can exist only in three or more dimensions. A simple example of a pair of skew lines is.....
A curved surface is considered a large set of points. Every point in the curve has two neighbors excluding the endpoints. Plane Surface is a flat surface in which a straight line joining any two of its points lies entirely on that surface. It’s a bit difficult to visualize a plane because.....
In mathematics, solid geometry is the traditional name for the geometry of three-dimensional Euclidean space. Examples like cones, cylinders, prisms, pyramids, polyhedra, and spheres. Solid geometry also includes the study of points, lines, shapes, and regions in relation to solids and.....
The definitions of a plane curve like circle, parabola, ellipse etc. are based on the concept of the locus. For example, the locus of points that are 1cm from the origin is a circle of radius 1cm centered on the origin, since all points on this circle are 1cm from the origin. If a point [….....
Introduction of locus – math: The concept of locus – math is very important in analytical geometry. The definitions of a plane curve like circle, parabola, ellipse etc. are based on the concept of the locus. So, a locus is a set of points satisfying a certain condition. For example, the locus.....
Apollonius’ theorem is an elementary geometry theorem relating the length of a median of a triangle to the lengths of its sides. It states that “the sum of the squares of any two sides of any triangle equals twice the square on half the third side, together with twice the square on .....
Polar Co-ordinates are widely used in higher mathematics as well as in other branches of science. In polar co-ordinate system, the position of a point on the reference plane is uniquely determined referred to a fixed point on the plane and a half line drawn through the fixed point. The fixed .....