Maths project 2024 for mathematics grade 8

maths

1. Maths project 2024-2025 TOPIC:REPRESENTING 3D IN 2D GROUP:BRAHMAGUPTA CLASS:VIII J

2. About Brahmagupta Brahmagupta was an Indian mathematician and astronomer. He is the author of two early works on mathematics and astronomy: the Brāhmasphuṭasiddhānta, a theoretical treatise, and the Khaṇḍakhādyaka, a more practical text .

3. Contribution of Brahmagupta in the field of Mathematics He was the first to explain how to use the numeral zero and negative numbers in mathematical calculations. He also came up with several new ideas in geometry, including a method to calculate the area of a cyclic quadrilateral known as Brahmagupta's Formula . developing rules for arithmetic operations involving zero, laying the foundation for modern mathematical notation. Brahmagupta's work also included advancements in algebra, geometry, and trigonometry, furthering the understanding of complex mathematical concepts during his time.

4. Representing 3D in 2D Introduction A two-dimensional (2D) object is an object that only has two dimensions, such as a length and a width, and no thickness or height. A three-dimensional (3D) object is an object with three dimensions: a length, a width, and a height. The flat sides of three-dimensional objects are two-dimensional shapes . Two-dimensional refers to something that exists only in a plane, an object with length and width but no depth. A two-dimensional, or 2D, object is a flat object that has length and width but no depth.

5. Difference between 2d and 3d Aspect 2d 3d Parameters 2D Shapes 3D Shapes Full-Form The term 2D is an acronym for two-dimensional. The term 3D is an acronym for three-dimensional. Dimensions Such shapes have a total of two dimensions. Such shapes have a total of three dimensions. Mathematical Axes They exist on the X-axes and the Y-axes. They exist on the X, Y, and Z-axes. Area and Volume These shapes only occupy an area. These shapes occupy both area and volume because they have a depth/ height. Type of View The 2D shapes give us a simple view of any object. The 3D shapes give us an architectural view of any object. Visibility of Edges Every edge is very clearly visible in the case of 2D shapes. Some of the edges stay hidden and are not visible in the case of 3D shapes. Ease of Explanation It is very easy to explain a 2D shape because all of its edges are visible to us. We can only explain the outer dimensions of a 3D shape because the rest of the edges are not visible to us. Detailing One can draw details on a 2D shape without any hassle. It is very difficult to draw details in a 3D shape. Ease of Drawing 2D shapes are very basic, thus easy to draw. 3D shapes are comparatively more complex and can sometimes be difficult to draw when combined together. Examples A few examples of the 2D shapes are rectangle, square, circle, triangle, or any other polygon. A few examples of the 3D shapes are cuboid, cube, sphere, cone, prism, cylinder, pyramid, etc.

6. CUBE and Cuboid   A cube is a three-dimensional solid object bounded by six square faces. It has twelve edges and eight vertices. It can be represented as the rectangular cuboid with six faces are all squares, and parallelepiped with the edges are all equal.  a cuboid is a quadrilateral-faced convex hexahedron. "Cuboid" means "like a cube", in the sense of a convex solid which can be transformed into a cube by adjusting the lengths of its edges and the angles between its adjacent faces

7. Sphere and Pyramid A sphere is a geometrical object that is a three-dimensional analogue to a two-dimensional circle. Formally, a sphere is the set of points that are all at the same distance r from a given point in three-dimensional space. That given point is the center of the sphere, and r is the sphere's radius. A pyramid is a polyhedron formed by connecting a polygonal base and a point, called the apex. Each base edge and apex form a triangle, called a lateral face. It is a conic solid with a polygonal base. Many types of pyramids can be found by determining the shape of bases, or cutting off the apex.

8. Nets A net is a flattened out three-dimensional solid. It is the basic skeleton outline in two dimensions, which can be folded and glued together to obtain the 3D structure. Nets are used for making 3D shapes