The document discusses the mathematics project for 2024-2025 focused on representing 3D shapes in 2D, highlighting the contributions of the Indian mathematician Brahmagupta in areas such as the use of zero, negative numbers, and geometric formulas. It distinguishes between two-dimensional (2D) and three-dimensional (3D) shapes, explaining their characteristics, examples, and complexities in representation. The document further elaborates on specific 3D shapes like cubes, cuboids, spheres, and pyramids, and introduces the concept of nets in 3D geometry.

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