What is area in mathematics?
Area is the measure of a region's size on a surface. It is the two-dimensional analogue of the length of a curve, which is one-dimensional, and the volume of a solid, which is three-dimensional.
Questions about Area
Short answers, pulled from the story.
What is the SI unit of area?
The standard unit of area in the International System of Units is the square metre, written m2, which is the area of a square whose sides are one metre long. The square metre is considered an SI derived unit.
Who first proved the area of a circle relates to its diameter?
In the 5th century BCE, Hippocrates of Chios was the first to show that the area of a disk is proportional to the square of its diameter, though he did not identify the constant of proportionality. In the same century, Eudoxus of Cnidus found that a disk's area is proportional to its radius squared.
How did Archimedes find the area of a circle?
Archimedes showed in Measurement of a Circle that the area inside a circle equals that of a right triangle whose base has the length of the circle's circumference and whose height equals the radius, yielding pi r squared. He approximated pi by inscribing and circumscribing polygons and repeatedly doubling their number of sides.
How many square feet are in an acre?
One acre equals 4,840 square yards, or 43,560 square feet. An acre is approximately 40% of a hectare.
What is a barn unit of area used for?
A barn is a unit of area equal to ten to the minus 28 square metres, used on the atomic scale. The barn is commonly used in describing the cross-sectional area of interaction in nuclear physics.
Why is the surface area of a sphere hard to calculate?
A sphere has nonzero Gaussian curvature, so it cannot be flattened out the way a cylinder or cone can. The formula for the surface area of a sphere was first obtained by Archimedes in his work On the Sphere and Cylinder.