NCERT Class 9 Mathematics Ganita Manjari: Chapter 5 — I'm Up and Down, and Round and Round
This chapter, "I'm Up and Down, and Round and Round," from NCERT's Class 9 Mathematics (Ganita Manjari) textbook, explores the fascination with shapes, particularly circles, inspired by nature. It highlights how humans observed circular patterns in phenomena like raindrops, the sun, and the moon, leading to the mathematical definition of a circle. The chapter defines a circle as the set of all points equidistant from a central point, introducing terms like 'centre,' 'radius,' 'chord,' and 'diameter.' It emphasizes that these geometric concepts are understood within a two-dimensional plane. This foundational understanding of circles is crucial for further mathematical studies in geometry and prepares students for CBSE examinations.
Quick info
| Board | CBSE / NCERT |
|---|---|
| Class | Class 9 |
| Subject | Mathematics |
| Book | Ganita Manjari |
| Chapter | Chapter 5 — I'm Up and Down, and Round and Round |
| Language | English |
| PDF type | NCERT Textbook |
| Session | CBSE 2026 |
| Reading time | 2 minutes |
| Word count | 398 |
Learning outcomes
- Understand the historical and natural inspiration behind geometric shapes, especially circles.
- Define a circle based on its equidistant points from a centre.
- Identify and define key circle components: centre, radius, chord, and diameter.
- Recognize that geometric shapes are studied within a two-dimensional plane.
Vocabulary
| Word | Meaning |
|---|---|
| Geometric patterns | Arrangements of shapes and lines that follow mathematical rules. |
| Circle | The set of all points on a plane that are equidistant from a given point (the centre). |
| Centre | The fixed point from which all points on the circle are equidistant. |
| Radius | The distance from the centre to any point on the circle. |
| Locus of points | A set of points that satisfy a given condition. |
| Chord | A line segment connecting two points on a circle. |
| Diameter | A chord that passes through the centre of the circle. |
| Plane | A flat, two-dimensional surface. |
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Practice questions
- What is the definition of a circle? Answer: A circle is the set of all points on a plane that are equidistant from a given point (the centre).
- What is the distance from the centre to any point on the circle called? Answer: Radius.
- What is a chord that passes through the centre of a circle called? Answer: Diameter.
- Give an example of a shape inspired by nature mentioned in the chapter. Answer: Circle (e.g., from raindrops on water, the sun, the moon).
Frequently asked questions
What are some examples of circles found in nature?
Circles can be observed when raindrops fall on water, in the cross-section of a plant stem, the inflorescence of a sunflower, the full moon, and the sun.
What is the fundamental property of all circles?
Every circle has a centre, and all points on the circle are at an equal distance from this centre.
How is a circle defined mathematically?
A circle is defined as the set of all points on a plane that are equidistant from a given point, which is called the centre.
What is a chord in a circle?
A chord is a line segment that connects any two points on the circle.
What is the longest chord of a circle called?
A chord that passes through the centre of the circle is called a diameter, which is the longest possible chord.
What does 'locus of points' mean in relation to a circle?
It means the set of points that satisfy a specific condition, and for a circle, the condition is being equidistant from a central point.
Related resources
Important topics
Topics covered
NCERT Class 9 Mathematics — Ganita Manjari — Chapter 5 — I'm Up and Down, and Round and Round. Verified by NCERT Help Editorial Team. Reviewed on 29 Jul 2026. Last updated 10 Aug 2026.