What are Mathematical shapes ?
Mathematical shapes are geometric figures or structures that are defined by mathematical equations or algorithms. Some common examples include:
▸ Circle
▸ Rectangle
▸ Square
▸ Right triangle
▸ Triangle
▸ Rhombus
▸ Ellipse
▸ Hexagonm
▸ Parallelogram
▸ Trapezium
▸ Cylinder
▸ Cube
▸ Semi-Circle
▸ Arrow
▸ Pentagon
▸ Ring
▸ Crescent
▸ Cross
Mathematical shapes Chart
Mathematical Shapes List With Pictures
| Mathematical Name in English | Mathematical Name in Hindi | Mathematical Pictures |
|---|---|---|
| Circle | चक्र, वृत्त |  |
| Rectangle | आयत |  |
| Square | वर्गाकार |  |
| Right triangle | समकोण त्रिभुज |  |
| Triangle | त्रिकोण |  |
| Rhombus | विषमकोण |  |
| Ellipse | दीर्घवृत्त |  |
| Hexagon | षट्कोण |  |
| Parallelogram | समान्तर चतुर्भुज |  |
| Trapezium | समलम्ब |  |
| Cylinder | बेलनाकार |  |
| Cube | घन |  |
| Semi-Circle | अर्ध-चक्र |  |
| Arrow | तीर |  |
| Pentagon | पञ्चभुज |  |
| Ring | छल्ला |  |
| Crescent | अर्धचन्द्राकार |  |
| Cross | जमा चिह्न |  |
Definition of Mathematical Shapes
☛ Circle (चक्र, वृत्त)
A circle is a two-dimensional geometric shape that consists of all points that are the same distance away from a central point, known as the center of the circle. The distance from the center to any point on the circle is called the radius of the circle. A circle can be defined mathematically by the equation x^2 + y^2 = r^2, where r is the radius and (x, y) are the coordinates of any point on the circle. Circles have several important properties, including:
● Circumference: the length of the boundary of the circle.
● Diameter: the longest distance across the circle, passing through the center.
● Area: the amount of space enclosed by the circle, defined as πr^2, where π is approximately equal to 3.14.
● Chords:straight lines connecting two points on the circle.
● Secants:lines that intersect the circle at two points.
● Tangents:lines that touch the circle at exactly one point.
☛ Rectangle (आयत)
A rectangle is a two-dimensional geometric shape that has four sides, four right angles, and opposite sides that are equal in length. A rectangle can be defined mathematically by its length (l) and width (w), and its area is equal to l × w. Rectangles have several important properties, including:
● Perimeter: the total length of the four sides of the rectangle, equal to 2l + 2w.
● Diagonal: the line segment connecting opposite corners of the rectangle, with length equal to the square root of l^2 + w^2.
● Aspect ratio: the ratio of the length to the width, which determines the shape of the rectangle.
● Midpoint:the point at the center of the rectangle, which is equidistant from all four corners.
Rectangles are commonly used in many areas of mathematics and science, including geometry, computer graphics, and engineering design. They are also used in everyday life, such as in the design of windows, doors, and rooms.
☛ Square (वर्गाकार)
A square is a two-dimensional geometric shape that has four equal sides and four right angles. It is a special case of a rectangle in which the length and width are equal. A square can be defined mathematically by its side length (s), and its area is equal to s^2. Squares have several important properties, including:
● Perimeter: the total length of the four sides of the square, equal to 4s
● Diagonal: the line segment connecting opposite corners of the square, with length equal to the square root of 2 times the side length (√2s).
● Aspect ratio: equal to 1, which means the shape is perfectly symmetrical.
● Midpoint:the point at the center of the square, which is equidistant from all four corners.
Squares are commonly used in many areas of mathematics and science, including geometry, computer graphics, and engineering design. They are also used in everyday life, such as in the design of floor tiles, blocks, and computer icons.
☛ Right triangle (समकोण त्रिभुज)
A right triangle is a type of triangle that has one angle that measures exactly 90 degrees, known as the right angle. The other two angles are called the acute angles. The sides of a right triangle can be related using the Pythagorean theorem, which states that the sum of the squares of the two shorter sides (the legs) is equal to the square of the longest side (the hypotenuse). This can be written mathematically as a^2 + b^2 = c^2, where a and b are the lengths of the legs and c is the length of the hypotenuse. Right triangles have several important properties, including:
● Perimeter: the total length of the three sides, equal to a + b + c.
● Area: half of the product of the lengths of the legs (A = 1/2 ab).
● Trigonometry:the ratios of the lengths of the sides in a right triangle are the basis for trigonometry, which is a branch of mathematics that deals with the relationships between angles and sides in triangles.
● Similar triangles: two triangles are similar if their angles are equal, which can be used to solve problems involving ratios of lengths and areas.
● Pythagorean triples: sets of three positive integers (a, b, c) that satisfy the equation a^2 + b^2 = c^2.
● Special right triangles: some right triangles have specific ratios of sides, such as the 30-60-90 triangle, which has sides in the ratio 1:√3:2, and the 45-45-90 triangle, which has sides in the ratio 1:1:√2.
Right triangles are commonly used in many areas of mathematics and science, including geometry, engineering, and navigation, and are also used in everyday life to solve problems involving distances and angles.
☛ Triangle (त्रिकोण)
A triangle is a two-dimensional geometric shape that has three sides and three angles. The sum of the interior angles of a triangle is always 180 degrees. Triangles are classified based on the lengths of their sides or the measures of their angles. Some common types of triangles include:
● Equilateral triangle: triangle with three equal sides.
● Isosceles triangle: a triangle with two equal sides.
● Scalene triangle: a triangle with three unequal sides.
● Right triangle: a triangle with one angle equal to 90 degrees.
● Acute triangle: a triangle with all interior angles less than 90 degrees.
● Obtuse triangle: a triangle with one interior angle greater than 90 degrees.
Triangles have several important properties, including:
● Perimeter: the total length of the three sides.
● Area: the amount of space enclosed by the triangle, which can be calculated using the formula 1/2bh, where b is the length of the base and h is the height.
● Median: a line segment connecting a vertex of the triangle to the midpoint of the opposite side.
● Altitude: a line segment connecting a vertex of the triangle to the opposite side, perpendicular to that side.
● Circumcenter: the center of the circle that passes through all three vertices of the triangle.
Triangles play an important role in many areas of mathematics, including geometry, trigonometry, and engineering, and are used to model real-world objects and solve mathematical problems.
☛ Rhombus (विषमकोण)
A rhombus is a two-dimensional geometric shape that has four equal sides and four angles equal to 90 degrees. It is a special case of a parallelogram in which all sides are equal in length. A rhombus can be defined mathematically by its diagonals, which bisect each other at right angles and are equal in length (d1 and d2). The area of a rhombus can be found using the formula A = d1 * d2 / 2.
Rhombus have several important properties, including:
● Perimeter: the total length of the four sides of the rhombus, equal to 4s, where is the length of a side.
● Angles: the angles between its diagonals are equal and are equal to half the measure of its interior angles.
● Aspect ratio: equal to 1, meaning the shape is perfectly symmetrical.
● Incenter: the center of the incircle, which is the largest circle that can be inscribed within the rhombus.
● Symmetry: the rhombus is a symmetrical shape, meaning it has rotational symmetry about its center.
● Midpoint the point at the center of the rhombus, which is equidistant from all four vertices.
Rhombus are commonly used in many areas of mathematics and science, including geometry, computer graphics, and engineering design. They are also used in everyday life, such as in the design of tiles, patterns, and shapes.
☛ Ellipse (दीर्घवृत्त)
An ellipse is a two-dimensional geometric shape that resembles a flattened circle. It is defined as the set of all points such that the sum of the distances from the two foci is constant. An ellipse can be mathematically defined by its semi-major axis (a), semi-minor axis (b), and its center (h, k). The semi-major axis is the length of the longest diameter of the ellipse, while the semi-minor axis is the length of the shortest diameter.
Ellipses have several important properties, including:
● Perimeter: can be approximated using the formula P = π(3a + 3b - √((3a + b)(a + 3b))).
● Foci: two points that define the shape of the ellipse, and the sum of the distances from any point on the ellipse to the foci is constant.
● Eccentricity:a measure of how "flattened" the ellipse is, ranging from 0 for a circle to 1 for a degenerate ellipse that is a straight line.
● Aspect ratio:equal to a/b, which is the ratio of the lengths of the semi-major and semi-minor axes.
● Area: equal to πab.
Ellipses play a significant role in many areas of mathematics and science, including astronomy, physics, and engineering. They are also used in everyday life, such as in the design of roads and stadium seating.
☛ Hexagon (षट्कोण)
A hexagon is a two-dimensional geometric shape that has six sides and six angles. Hexagons can be classified into different types based on their side lengths and angles, including:
● Regular hexagons: hexagons with six equal sides and six equal angles.
● Irregular hexagons: hexagons with unequal sides and/or angles.
The area of a regular hexagon can be found using the formula (3 √3)/2a^2, where a is the length of a side. The perimeter of a hexagon is equal to the sum of the lengths of its sides, or 6a for a regular hexagon.
Hexagons have several important properties, including:
● Perimeter: the total length of the six sides of the hexagon, equal to 6 times the length of one side in a regular hexagon.
● Area: the total size of the interior of the hexagon, which can be found using the formula A = (3√3/2)s^2 for a regular hexagon with side length.
● Interior angles: the sum of all interior angles is equal to 720 degrees, where each interior angle measures 120 degrees.
● Exterior angles: the sum of all exterior angles is equal to 360 degrees, where each exterior angle measures 60 degrees.
● Vertices: the points where the sides of the hexagon meet.
● Diagonals: the total number of diagonals in a regular hexagon is 9.
Hexagons play an important role in many areas of mathematics and science, including tessellations, computer graphics, and engineering. They are also used in everyday life, such as in the design of honeycomb patterns and fabric patterns.
☛ Parallelogram (समान्तर चतुर्भुज)
A parallelogram is a two-dimensional geometric shape that has four sides and four angles. It is defined by two pairs of parallel sides, and opposite sides are equal in length. A parallelogram can be described mathematically by its base (b) and height (h), and its area is equal to bh.
Parallelograms have several important properties, including:
● Perimeter: the total length of the four sides of the parallelogram, equal to 2 times the sum of the lengths of its base and height.
● Area: the total size of the interior of the parallelogram, equal to bh.
● Angles:the opposite angles are equal in measure, and adjacent angles add up to 180 degrees.
● Diagonals: the two diagonals of a parallelogram bisect each other and are equal in length.
Parallelograms are commonly used in many areas of mathematics, such as geometry, trigonometry, and engineering. They are also used in real-world applications, such as in the design of building foundations and the analysis of stress and strain in materials.
☛ Trapezium (समलम्ब)
A trapezium (also known as a trapezoid in some countries) is a two-dimensional geometric shape that has four sides and four angles. It is defined as having at least one pair of parallel sides, called the bases, with the other two sides slanting towards each other. A trapezium can be described mathematically by its bases (a and b) and height (h), and its area is equal to (a + b)h/2.
Trapeziums have several important properties, including:
● Perimeter: the total length of the four sides of the trapezium, equal to the sum of the lengths of its bases and its sides.
● Angles: : the angles between its sides and its bases vary in measure, and the sum of its interior angles is 360 degrees.
● Area: the total size of the interior of the trapezium, equal to (a + b)h/2.
Trapeziums are commonly used in many areas of mathematics, such as geometry and trigonometry. They are also used in real-world applications, such as in the design of bridges and the analysis of surfaces in engineering and surveying.
☛ Cylinder (बेलनाकार)
A cylinder is a three-dimensional geometric shape that has two parallel, congruent circular bases and a lateral surface that connects the two bases. It can be described mathematically by its height (h) and radius (r), and its volume is equal to πr^2h.
Cylinders have several important properties, including:
● Volume: the total space inside the cylinder, equal to πr^2h.
● Surface area: the total area of the lateral surface and the two circular bases, equal to 2πrh + 2πr^2.
● Height: the perpendicular distance between the two bases.
● Radius: the distance from the center of one of the circular bases to the lateral surface.
Cylinders are commonly used in many areas of mathematics, such as geometry and calculus. They are also used in real-world applications, such as in the design of containers, pipes, and engine cylinders.
☛ Cube (घन)
A cube is a three-dimensional geometric shape that has six square faces and twelve straight edges. It is a special type of rectangular prism, in which all sides are equal in length. A cube can be described mathematically by its side length (s), and its volume is equal to s^3.
Cubes have several important properties, including:
● Volume: the total space inside the cube, equal to s^3.
● Surface area: the total area of the six square faces of the cube, equal to 6s^2.
● Edge length: the length of each of the twelve straight edges of the cube, equal to s.
● Vertices: eight points where the edges of the cube meet, called vertices.
● Diagonal length: the length of a diagonal from one vertex to an opposing vertex of the cube, equal to the square root of 3 times the edge length.
Cubes are commonly used in many areas of mathematics, such as geometry, linear algebra, and computer graphics. They are also used in real-world applications, such as in the design of building structures, storage containers, and dice.
☛ Semi-Circle (अर्ध-चक्)
A semi-circle is a two-dimensional geometric shape that is half of a circle. It is defined by a center point and a radius, and its boundary is made up of points that are equidistant from the center and the circumference of the original circle. A semi-circle can be described mathematically by its radius (r), and its area is equal to πr^2/2.
Semi-circles have several important properties, including:
● Area: the total size of the interior of the semi-circle, equal to πr^2/2.
● Circumference: half of the circumference of the original circle, equal to πr.
● Chord: a straight line connecting any two points on the boundary of the semi-circle. The length of the chord is equal to the diameter of the original circle.
● Arc: a portion of the circumference of the original circle, defined by two points on the boundary of the semi-circle.
Semi-circles are commonly used in many areas of mathematics, such as geometry, trigonometry, and calculus. They are also used in real-world applications, such as in the design of curves and arcs, and in the analysis of circular motion.
☛ Arrow (तीर)
An arrow is a graphical symbol used to represent direction or movement. It is often used in diagrams, graphs, and maps to indicate the direction of flow or to point to a specific location. Arrows can be represented in various styles and shapes, but a common representation is a thin, straight line with a triangular head at one end.
Arrows have several uses, including:
● Indicating direction: Arrows are used to show the direction of movement, flow, or rotation.
● Pointing to a specific location: Arrows can be used to draw attention to a particular location or item in a diagram or image.
● Representing a mathematical vector: In mathematics, arrows can be used to represent vectors, which have both magnitude and direction.
Arrows are widely used in a variety of fields, including engineering, architecture, geography, and physics, as well as in many different types of diagrams, graphs, and maps. They are an essential tool for visual communication and understanding.
☛ Pentagon (पञ्चभुज)
A pentagon is a two-dimensional geometric shape that has five straight sides and five vertices (corners). It can be described mathematically by the length of its sides and its interior angles. The sum of the interior angles in a pentagon is equal to 540 degrees.
Pentagons have several important properties, including:
● Perimeter: the total length of the sides of the pentagon, equal to the sum of the lengths of the five sides.
● Area: the total size of the interior of the pentagon, which can be found using the formula for the area of a regular pentagon or by dividing the pentagon into triangles and finding the sum of their areas.
● Interior angles: five interior angles, with the sum of all five equal to 540 degrees.
● Diagonals: line segments connecting non-adjacent vertices of the pentagon. The number of diagonals in a pentagon is equal to ten.
Pentagons are commonly used in many areas of mathematics, such as geometry, trigonometry, and graph theory. They are also used in real-world applications, such as in the design of regular polygons, in computer graphics and image processing, and in cryptography.
☛ Ring (छल्ला)
A ring is a two-dimensional geometric shape that consists of a circular region enclosed by a curved line. It is similar to a circle, but with a hole in the middle. The hole in the middle of the ring is usually referred to as the "interior" of the ring. A ring can be described mathematically by its inner and outer radii, and its area can be found by subtracting the area of the inner circle from the area of the outer circle.
Rings have several important properties, including:
● Area: the total size of the interior of the ring, which can be found by subtracting the area of the inner circle from the area of the outer circle.
● Circumference: the total length of the curved line that encloses the interior of the ring, which is equal to the sum of the circumferences of the inner and outer circles.
● Inner and outer radii: the distances from the center of the ring to the inner and outer edges, respectively.
Rings are commonly used in many areas of mathematics, such as geometry and topology, as well as in real-world applications, such as in the design of annular gears and in the analysis of circular motion. They are also used as symbols, such as in the representation of rings in jewelry and in the Olympic symbol.
☛ Crescent (अर्धचन्द्राकार)
A crescent is a shape resembling a moon at various phases, particularly a shape resembling the moon in its first or last quarter. In mathematics, a crescent can be described as a partially enclosed curved shape, with two straight sides that meet at an angle and curve outward to form a crescent-like shape.
Crescents have several important properties, including:
● Length: the total length of the curved line that defines the shape of the crescent.
● Area: the total size of the interior of the crescent, which can be found using the methods of integral calculus.
● Angle: the angle formed by the two straight sides of the crescent, which determines the shape of the crescent.
Crescents are commonly used in many areas of mathematics, such as geometry, trigonometry, and calculus, as well as in real-world applications, such as in the design of curved objects and in the analysis of curved motion.
☛ Cross (जमा चिह्न)
A cross is a shape consisting of two intersecting lines, usually perpendicular to each other. In mathematics, a cross can be described as the intersection of two lines, one horizontal and one vertical.
Crosses have several important properties, including:
● Length: the total length of the intersecting lines.
● Angle: the angle formed by the two intersecting lines, which is usually 90 degrees (a right angle).
● Center: the point at which the two lines intersect, which is also known as the origin in a Cartesian coordinate system.
Crosses are commonly used in many areas of mathematics, such as geometry, trigonometry, and linear algebra, as well as in real-world applications, such as in the design of crosses for religious symbols and in the representation of the Cartesian coordinate system.