User:SabrinaPannu
Hi, my name is Sabrina and I'm in the Faculty of Arts :)
The Pythagorean Theorem
The Pythagorean Theorem was discovered by the famous Greek mathematician and philosopher Pythagoras. However, there is some controversy in the mathematical community as some suggest Pythagoras may have stolen his famous formula from the Babylonians. The theorem is commonly written as an equation, known as the Pythagorean equation: a2 + b2 = c2. In this simplistic formula, the letters refer to the three sides of a right-angled triangle with a and b signifying the sides of the triangle and c representing the hypotenuse. Essentially, the Pythagorean Theorem allows us to find the missing length of the side of a right triangle and is taught in geometry classes globally as it has extraordinary relevance to our daily lives. It is widely used in the field of engineering. The Pythagorean Theorem also has hundreds of proofs giving it immense credibility; in fact, it has more proofs than any other mathematical theorem in the world.
Sources: Wikipedia-Pythagorean Thereom[1]
Calculus in Economics
Calculus is the branch of mathematics concerning the identification and properties of derivatives and integrals of functions and has many practical applications in many fields. One of these fields is economics. Economics and mathematics are closely related as calculus is essentially the language of economics. Calculus is applied in even the basics of microeconomics when firms are trying to maximize their profit, or when individuals are looking to increase utility. A firm produces outputs through the basic principle that marginal cost = marginal revenue. The term “marginal”in economics can be thought of as synonymous with the “derivative of ” as in calculus. The profit is revenue minus cost and in order to maximize it, the equation must be set to zero. Therefore profit is maximized when both marginal cost and marginal revenue are equal to each other. Calculus aids business owners to figure out marginal revenues and costs so they can in turn maximize their profits.
Here is a video showing how calculus can be used to determine marginal revenue and cost:
| Economics: Marginal Cost and Revenue |
|---|
|
|
Integrals are also predominant in economics, especially in the areas of consumer and producer surplus and deadweight loss. Calculus is also applied in the topics of elasticity, for example when given a formula to find elasticity rather then a numerical value, the derivative of that formula must be found in order to do so. In its most basic form, the logic and deductive knowledge theorized in calculus is transcended through the application of economics. Logic and problem solving are prevalent in both micro and macro economics in analyzing how market forces work, externalities, growth rates, elasticity, and etc. The techniques and skills I gain though my calculus courses will definitely be a great asset to my studies of economics.