History and Background


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History of Area and Volume


The concepts of area and volume and calculating them have been around for millenia. Roger Yarnell, in his article titiled 'Area and Volume: Where Do the Formulas Come From?', explains that 'The earliest beginnings of geometry can be traced back to around 3000 BC to ancient Egypt and Mesopotamia. They had used lengths, angles, areas, and volumes for construction and surveying purposes.' Then brilliant mathematicians continued to develop these concepts over time until they became what we know today. Archimedes is credited with finding the volume of a sphere around 250 B.C. He realized that using water displacement could tell what the volume of an object is. Overtime, as mathematics continued to develop, mathematicians continued to get more precise with their calculations. Eventually in the early 17th Century, Bonaventura Cavalieri used the philosophy of modern integral calculus to calculate volume. He developed a principle, that he named after himself, which said 'that using thinner and thinner slices of the shape would make the resulting volume more and more accurate. Taking Cavalieri’s principle, we can derive the formulas for volume using calculus.