User:GracieMann

Hi my name is gracie and I am currently studying commerce at Sauder.

Calculus in Fashion

In an article I came across recently it discussed how major fashion designer Michael Kors was inspired by linear derivatives for his 2010 Spring collection. It got me thinking about how influential math really is in today’s world. I was always told in high school how math was integral to just about any job in the real world but I never fully believed that I would have to find the derivative of a function in order to do the type of work I wanted to. Fashion is always something I have been passionate about, currently I am in the commerce program in order to learn the necessary skills to run the business side of fashion. In reality basic math is a key element of fashion design- when creating the clothes measurements need to be taken, circumferences are divided in order to find appropriate sizing, sequences like the Fibonacci Sequence can be related into pattern designs to create added texture. On the contrary within business math forms are much more complex and calculus is further present. In order to find out the marginal cost of producing dresses within a fashion house you can use calculus. Marginal cost is the cost of producing one more additional unit and is approximated by the rate of change of the cost function which can be denoted as C(x). The marginal cost function is the derivative of the cost function and we can denote this by C’(x). Given the equation C(x) = 500+10x+0.2x^2 for the cost of producing x amount of dresses we can find the cost by finding the derivative of the function. The derivative is represented by C’(x)= -0.4x+10. If you want to find the cost of producing 300 dresses you can do this by plugging it into the derivative of the function which would give us the marginal cost as $130. For finding each additional marginal cost for say 500 dresses you could plug the 500 in for x. Being able to find the marginal cost you can see how much money it is going to cost the company in order to produce another dress. This is helpful in setting the price on the product you are selling so you are able to account for the cost and still make a profit. Marginal cost is directly linked to all different types of industry and is not just found in fashion. There are many more applications of calculus in business such as average cost, and marginal revenue function. All in all calculus is present in our everyday lives no matter what your interest.

Sources Cited: http://www.trendhunter.com/trends/michael-kors-spring-2010

http://tutorial.math.lamar.edu/Classes/CalcI/BusinessApps.aspx

http://answers.yahoo.com/question/index?qid=20081103161841AAhvrKU

Pythagorean Theorem

Pythagoras, a famous and influential Greek philosopher who lived from ca. 570 to ca. 490 BCE, discovered the Pythagorean theorem. Pythagoras relied on the knowledge of others and drew his inspiration from famous philosophers such as Plato and Aristotle. Among being a philosopher and expert on soul after death he was also a mathematician. The Pythagorean theorem is a geometric idea that relates to the ability to find the length of one side of a right-angled triangle if given the other two lengths. He discovered that the longest side is made up of squaring the two shorter sides and adding them together. The theorem can be explained through an equation such as a^2+b^2=c^2. A and B represent the two shorter sides of the triangle and C represents the hypotenuse. An extension off his idea of the Pythagorean theorem is Pythagorean triples. Pythagorean triples are three positive integers that relate to the three sides in a Pythagorean triangle. An example of a few of these is the most widely used example of 3,4,5 and 5,12,13. The Pythagorean theorem is helpful to decipher lengths and areas of right-angled triangles.

Resources: http://plato.stanford.edu/entries/pythagoras/ http://en.wikipedia.org/wiki/Pythagorean_triple http://en.wikipedia.org/wiki/Pythagorean_theorem