Mathematics Essays

Perfect numbers are a set of integers whose divisors all add up to that number. The number six is one such perfect number since its divisors, one, two, and three all add up to six (1 + 2 + 3 = 6). The next perfect numbers are 28, 496 and …

Preferred language style: English(U.S.) Please Show all work. ( calculus 1 ) 1) Show that the given families of curves are orthogonal trajectories of each other. Sketch both families of curves on the same axes. x2 + y2 = r2, ax+ by= 0 The two equations are orthogonal trajectories of …

Proof by Induction Mathematical induction is an alternative way of proving mathematical theorems. Instead of using analysis and tractability, mathematical induction relies on verifying base truths and showing that the theorem holds for other parameters based on these base truths. Mathematical Induction usually starts by showing that the theorem is …

An integrated study is one in which students generally look at awareness in an assortment of subject matter correlated to specific characteristic of their background It perceives relations between the communication arts, mathematics,  humanities, social studies, natural sciences music, as well as art. Dexterity and information are expanded in addition …

The 18th century mathematician Leonard Euler is considered a pioneering mathematician and physicist. He is remembered for his contributions to calculus and graph theory, many of which bear his name. Some of the concepts attributed to Euler include Euler cycles and paths in graph theory, Euler equations in fluid dynamics, …

Number theory, or higher arithmetic, is the branch of mathematics that studies natural numbers and similar objects. It’s uses stretch from the theoretical to the practical; from investigations of the properties of integers to stability questions as important as “Will the planets continue to orbit in well-defined zones without collision?”[1] …

An example of an exponential function is the voltage as a function of time Vf(t) as the capacitor C1 discharges from an initial voltage Vi to a resistive load R1. The circuit of this is shown below Figure 1. Discharge of Capacitor Where Vf is the final voltage Vi is …

     Recognizable it is that the term Aromatherapy is being used nowadays. It is but one of the blooming industries at present and is seemingly growing more each year. It is being offered in health spas which seem to emerge like mushrooms everywhere. It may also be done personally …

I’m at a classroom trying to solve this math problem given by you. Where should I go now can you help me, I cannot take this anymore. Yeah, I, I know its hard to remember The lessons that you have taught Its even harder to picture that I can pass …

For those who are unaware, at least 1 and 2 are thanks to Georg Cantor and his invention of set theory. He had to endure a lot of resistance from the mathematical luminaries of his day – Kronecker and apparently, even Poincaré! Like Nietzsche, he died in a mental institution, …