minimal entity page
region r
[region r|region r] is a circle with radius 2 and area 4 units².
Definition
region r is a circle with radius 2 and area 4 units². The Symmetry Principle states that if region r is symmetric about a line, its centroid lies on that line.
Mechanism
region r involves circular motion around the y-axis with a radius of 4 units. The distance traveled by the centroid is 8z units, equal to the circumference of the path.
Constraints
region r Theorem 6.11 states that if a region R is symmetric about a line, then its centroid lies on that line. This principle applies to symmetric regions and forms a basis for analyzing laminas.