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Which of the following options is true for the wheel of Theodorus?

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It doesn’t have any isosceles triangle.

The spiral chord is started with an isosceles triangle with each leg having length 2 units.

The spiral is stated with an isosceles right angle triangle each having unit length.

None of these

answer is C.

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Detailed Solution

Now let us first understand the wheel of Theodorus.
⇒ Now Let us draw two sides, both length 1 unit perpendicular to each other.
seo

⇒ Now connect the endpoints to form a triangle.
seo

⇒ Now we know that the sides are of length 1 unit.
⇒ Hence by Pythagoras theorem we have length of hypotenuse is

\sqrt{{1^{2} + 1}^{2}}

\sqrt{2}

⇒ Now again draw a unit side perpendicular to one end of the hypotenuse. Hence we get
seo

⇒ Now again join the two sides to form a triangle.
seo

⇒ Now in this new triangle, we have one length is

\sqrt{2}

and another is 1.
Hence we get the length of hypotenuse is

\sqrt{{(\sqrt{2})}^{2} + 1^{2}}

\sqrt{2 + 1}

\sqrt{3}

⇒ Now we continue these steps after 5 triangles we get a structure in the form of
seo

Now as we keep continuing this we can see the structure forming a wheel.
⇒ This is called the wheel of Theodore.
Now consider the given options
Hence option c is the correct option.
So, option (3) is correct.

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