Which one of the following is different from the remaining three ?

Which one of the following is different from the remaining three ?

Triangle
Square
Circle
Ellipse
This question was previously asked in
UPSC CAPF – 2016
The correct answer is Circle.
– Triangle and Square are polygons, which are closed figures formed by straight line segments.
– Circle and Ellipse are closed curved shapes, not polygons. They are also both conic sections (formed by intersecting a cone with a plane).
– This grouping places Triangle and Square in one category and Circle and Ellipse in another, which doesn’t allow one to be different from the other three.
– Let’s consider other properties:
– Triangle: Can have varying angles and side lengths (scalene, isosceles, equilateral). Curvature is concentrated at vertices.
– Square: All angles are 90 degrees, all sides equal. Constant zero curvature along sides, infinite curvature at vertices.
– Ellipse: Varying curvature along the curve.
– Circle: Constant curvature along the curve. A circle is a special case of an ellipse where the two foci coincide and the eccentricity is zero.
– The property that distinguishes the Circle from the other three is its constant curvature. Triangle, Square, and Ellipse all have curvature that varies or is concentrated at points (infinite curvature at vertices for polygons).
Other possible but less compelling distinctions could be made (e.g., minimum sides for polygon – Triangle, regularity – Square and equilateral Triangle are regular polygons, Circle is ‘most regular’ curve), but constant curvature provides a clear mathematical distinction that groups Triangle, Square, and Ellipse (non-constant/infinite curvature) against Circle (constant curvature).