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The shape of the wheel of Theodorus is a
A. Circle
B. Spiral
C. Triangle
D. Polygon

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Last updated date: 22nd Feb 2024
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IVSAT 2024
Answer
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Hint: In this problem, we have to find the shape of the Theodorus. We should know that, in geometry, the spiral of Theodorus (also called a square root spiral), is a spiral composed of right triangles placed edge to edge. It was named after Theodorus of Cyrene.

Complete step by step answer:
We should know that the spiral of theodorus starts with an isosceles right triangle with both legs of length 1, more right triangles are added, one leg the hypotenuse of the previous triangle, the other outside leg, always of length one and the shape looks like a spiral.
We should also know that Theodorus stopped his spiral at the triangle with the hypotenuse of \[\sqrt{17}\]. If the spiral is continued to infinitely many triangles, many more interesting characteristics are found.
In 1958, Erich Tueffel proved that no two hypotenuses will coincide, regardless of how far the spiral is continued. Also, if the sides of unit length are extended into a line, they will never pass through any of the other vertices of the total figure.

Therefore, from the above theory, we can say that the shape of the wheel of Theodorus is an option. B. Spiral.

Note: We should know that, in geometry, the spiral of Theodorus (also called a square root spiral), is a spiral composed of right triangles placed edge to edge. It was named after Theodorus of Cyrene. We should also know that Theodorus stopped his spiral at the triangle with the hypotenuse of \[\sqrt{17}\].