Question

1. which of the following is a famous example of a geometric fractal?

a. koch curve
b. cubic function
c. pythagorean triangle
d. spherical design

Explanation:

• Koch Curve: It is a well - known geometric fractal. A fractal is a geometric shape that has self - similarity at different scales. The Koch Curve is constructed by repeatedly replacing line segments with a more complex pattern, and it shows the characteristic of infinite detail and self - similarity.
• Cubic Function: A cubic function is a polynomial function of the form \(y = ax^{3}+bx^{2}+cx + d\) (\(a

eq0\)). It is a smooth curve (not a fractal) and does not have the self - similarity at different scales in the geometric sense like a fractal.

• Pythagorean Triangle: A Pythagorean triangle (right - triangle) is a geometric shape with sides \(a\), \(b\), \(c\) such that \(a^{2}+b^{2}=c^{2}\). It is a simple geometric figure and not a fractal.
• Spherical Design: A spherical design is a set of points on a sphere with certain optimality properties for numerical integration and interpolation on the sphere. It is not a fractal.

Answer:

A. Koch Curve