squash
13
Show how 5 can be represented on the nu
Classroom activity (Constructing the square root
spiral') : Take a large sheet of paper and construct
the 'square root spiral' in the following fashion. Start
with a point and draw a line segment OP, of unit
length Draw a line segment P,P. perpendicular to
OP, of unit length (see Fig. 1.9). Now draw a line
segment P.P perpendicular to OP, Then draw a line
segment P P. perpendicular to OP. Continuing in
this manner, you can get the line segment P P. by
drawing a line segment of unit length perpendicular to OP
square root spi
In this manner, you
depicting 2. 3. 4. ...
Fig. 1.9: Constructing
have created the points P. P....... P.... .. and joined them to create a beautiful sp
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Answer:
The spiral is started with an isosceles right triangle, with each leg having unit length. Another right triangle is formed, an automedian right triangle with one leg being the hypotenuse of the prior triangle (with length √2) and the other leg having length of 1; the length of the hypotenuse of this second triangle is √3. The process then repeats; the nth triangle in the sequence is a right triangle with side lengths √n and 1, and with hypotenuse √n + 1.
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