Square Root Spiral Activity

(Using JUMBO GEOMETRY BOX MAGNETIC – LKGM 404 Maths Kit under PM SHRI Scheme)

Aim:
To construct a Square Root Spiral (also known as Theodorus Spiral) using geometrical tools, and to understand square roots through geometrical visualization.

Kit Items Used:

• JUMBO GEOMETRY BOX MAGNETIC — LKGM 404 Maths Kit

• Magnetic ruler

• Magnetic compass

• Magnetic protractor

• Magnetic set squares

• Magnetic board

• Chalk or marker

• Pointer for explanation

(This kit is a precision model designed for demonstrating accurate geometric constructions in the classroom using magnetic tools, enabling clear, hands-on learning.)

Procedure:

1. Place a magnetic board vertically or flat, and fix the base point O.

2. Using the ruler, draw a line segment OA = 1 unit.

3. At point A, construct a perpendicular using the set square.

4. With A as the center and radius 1 unit, draw an arc to cut the perpendicular at point B. Now, OB = √2 units.

5. Using B as the center and OB as the radius, draw another perpendicular and mark point C such that OC = √3 units.

6. Continue this process:

   • Each new radius equals the square root of the next natural number.

   • Join the points sequentially (O → A → B → C → D...) to create the spiral.

7. Label all the distances clearly (√2, √3, √4, √5...) along the spiral path.

Observation:

• Each new line segment represents the square root of successive natural numbers.

• The spiral visually demonstrates that square roots are real, measurable quantities — not just abstract numbers.

• The distance from the center O to any point on the spiral is √n, where n is the step number.

Conclusion:

The Square Root Spiral is an excellent geometrical representation of square roots. This activity helps students understand that square roots — including irrational numbers — can be visualized as lengths in geometry, enhancing their conceptual clarity and spatial thinking.