Question

three students attempt to define what a circle is.
can you match the teachers comments to the definitions?
definition of a circle
rubys definition: a 3 - dimensional shape whc po indary onsists of all points equidis a fixed point (the ter).
shriyas definition: the set of all points in a 2d plane such that for every point in the set there is exactly one other point in the set that is d (call it diameter) units away.
abhisheks definition: the set of all points in a plane that are the same distance (radius) away from some given point (center).
teachers comments
you are correct. nicely done!
this is incorrect. for example, your definition also allows for the following shape, which is just part of a circle:
are you thinking of a sphere?

Explanation:

• Ruby's definition mentions a 3 - dimensional shape. A sphere is a 3 - dimensional object where all points on its surface are equidistant from the center. So, the comment “Are you thinking of a sphere?” matches Ruby's definition.
• Shriya's definition allows for shapes that are just parts of a circle (like a semicircle, where for every point on the semicircle, there is exactly one other point at a distance equal to the diameter). So, the comment “This is incorrect. For example, your definition also allows for the following shape, which is just part of a circle:” matches Shriya's definition.
• Abhishek's definition is the standard definition of a circle (a 2 - D set of points equidistant from a center point). So, the comment “You are correct. Nicely done!” matches Abhishek's definition.

Answer:

• Ruby's definition: Are you thinking of a sphere?
• Shriya's definition: This is incorrect. For example, your definition also allows for the following shape, which is just part of a circle:
• Abhishek's definition: You are correct. Nicely done!