what is the historical background of perimeter and area
Answers
Perimeter is the length of the closed boundary around/enclosing a region or space. The word “peri” is from Greek, means “around”. Archimedes approximated the perimeter of a circle with sum of sides of polygons of large number of sides.
Perimeters of shapes are found as and when new shapes are defined. This was not too difficult. The relation of area to perimeter also was explored for many shapes.
After integral calculus was developed, perimeters of complex shapes (2-d and 3-d) could be found with precision and with formulas. A term wetted perimeter is used by engineers (civil, mechanical and chemical). Also police and investigation agencies use the term perimeter. Also Chinese worked on the formula for perimeter. Most complex problem was to find perimeter of a circle. Other shapes were not so difficult.
====
Area is the amount of 2-dim space/region enclosed by a closed boundary or perimeter.
Hippocrates of Chios proved that the area of a circular disk is proportional to square of radius, in 5th century BCE. Euclid experimented with area of a circle too. Archmedis too worked with the area of circles using right angle triangles, hexagons and polygons by successively doubling the number of sides. Thus he approximated the circle with polygon of a large number of sides.
Hohann Heinrich Lamburt also worked on Pi which is related to the area of a circle divided by the square of its radius.
Heron of Alexandria gave a formula for the area of a triangle in year 60 CE. Aryabhata of India too expressed the area of a triangle in a formula in year 499. Greeks and Chinese too worked on areas of triangle.
Brahmagupta of India gave a formula for the area of a cyclic quadrilateral (with all 4 vertices on one circle) in 7th century AD. Germans Carl Bretschneider and Karl Christian Von Staudt gave a formula for any quadrilateral.
Rene Descartes developed the Cartesian coordinate system of (x,y). Gauss gave a formula for the area of a polygon with known vertex locations.
Areas of complex shapes could be found by integral calculus, even for surfaces in 3-dimensions.