Constructing a Square Root Spiral

Transcript

Constructing a Square Root Spiral A square root spiral (also called Spiral of Theodorus) looks like this Here, we use Pythagoras Theorem again and again to construct it Let's look at how to construct it step-by-step Draw base line 1 unit Step 1: Mark a center point (origin). Draw a straight horizontal line segment of exactly 1 unit. CONSTRUCTION STEP 1 Step 2: Using a protractor, draw a perpendicular line of 1 unit from the outer tip. Connect back to the origin to form a hypotenuse of .ONSTRUCTION STEP 2 Step 3: Using a protractor, draw a perpendicular line of 1 unit from the outer tip. Connect back to the origin to form a hypotenuse of .CONSTRUCTION STEP 3 Step 4: Using a protractor, draw a perpendicular line of 1 unit from the outer tip. Connect back to the origin to form a hypotenuse of .CONSTRUCTION STEP 4 Step 5: Using a protractor, draw a perpendicular line of 1 unit from the outer tip. Connect back to the origin to form a hypotenuse of .CONSTRUCTION STEP 5 Step 6: Using a protractor, draw a perpendicular line of 1 unit from the outer tip. Connect back to the origin to form a hypotenuse of .CONSTRUCTION STEP 6 Step 7: Using a protractor, draw a perpendicular line of 1 unit from the outer tip. Connect back to the origin to form a hypotenuse of .CONSTRUCTION STEP 7 Step 8: Using a protractor, draw a perpendicular line of 1 unit from the outer tip. Connect back to the origin to form a hypotenuse of .CONSTRUCTION STEP 8 Step 9: Using a protractor, draw a perpendicular line of 1 unit from the outer tip. Connect back to the origin to form a hypotenuse of .CONSTRUCTION STEP 9 Step 10: Using a protractor, draw a perpendicular line of 1 unit from the outer tip. Connect back to the origin to form a hypotenuse of .CONSTRUCTION STEP 10 Step 11: Using a protractor, draw a perpendicular line of 1 unit from the outer tip. Connect back to the origin to form a hypotenuse of .CONSTRUCTION STEP 11 Step 12: Using a protractor, draw a perpendicular line of 1 unit from the outer tip. Connect back to the origin to form a hypotenuse of . CONSTRUCTION COMPLETE Spiral of Theodorus Constructed! You can keep repeating these steps infinitely to construct the square root of any natural number geometrically!