how to make square root spiral

Question

Answer

Making a Square Root Spiral

A square root spiral is a type of spiral that is made up of a series of squares, each of which has a side length equal to the square root of the previous square's area. The spiral can be drawn using a compass and ruler, or with the help of a computer program.

Step-by-Step Guide

Start by drawing a square with a side length of your choice. Let's call this square A.

Next, draw a square next to square A, with a side length equal to the square root of the area of square A. Let's call this square B.

Draw another square next to square B, with a side length equal to the square root of the area of square B. Let's call this square C.

Continue this process, drawing squares with side lengths equal to the square root of the previous square's area, until you have the desired number of squares.

Connect the corners of the squares with a smooth curve to create the spiral.

Tips

Make sure to measure each square carefully, as errors in measurement can add up and affect the overall shape of the spiral.

Use a compass and ruler to ensure that each square is drawn accurately.

If using a computer program, make sure to set the dimensions of each square correctly to ensure that the spiral is drawn accurately.

Experiment with different starting square sizes to create spirals of different shapes and sizes.

Answer

Firstly take 1 unit and draw it as A to B.... then construct 90 degree from B with the measurement of the same unit u take previously( 1 unit) at C ..then join A to C
.... then again with sam process construct 90 degree at C withthe measurement of the same unit u take previously( 1 unit) at D and join it with again A ...so keep this process on till your spiral complete....

Hope so it will help u...

Answer

Objective
To make a square root spiral by using paper folding.

Prerequisite Knowledge
In a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
eg., √2 = √(12 +12). By using this Concept, we will represent irrational numbers on a number line by paper folding.

Materials Required
Tracing paper, pencil, geometry box.

Procedure
To represent √2 on a number line.

Draw a line OX on the tracing paper. Mark point O on one end and mark points 0, 1,2, 3, … at equal distances of 1 unit by paper folding.
Fold the paper along the line that passes through the point marked ‘1’ and perpendicular to the line OX, i.e., fold the paper in such a way that point ‘O’ coincides with point ‘2’. Make a crease and unfold it. From the point marked ‘1’, draw a line of length 1 unit moving along the crease. Mark the point as M such that PM = 1 unit. Join OM, clearly OM= √2 units.

Fold the paper along the line ( fold on point M in such a way that point O joined with any point lie on OX,) that passes through point M and perpendicular to OM at M. Make a crease and unfold it. From the point M, draw a line of 1 unit moving upward, along the crease. Mark the point as N such that MN = 1 unit. Join ON, where ON = √3.

Keep this process continuously to get √4, √5, √6, ……….

Result
In this way, we get a square root spiral pattern by using paper folding.

Learning Outcome
On the same plane, different irrational numbers can be represented on the number line by paper folding method.
By using Pythagora’s theorem students will be able to construct a square root spiral by paper folding method.

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