Variations On Curves

This monograph is the third in a series devoted to special topics in Mathematics; in particular those topics not covered in a standard High School mathematics core curriculum. As such, the target audience would be mathematically motivated and/or intellectually curious High School students and recreational mathematicians. No mathematics beyond Introductory Calculus is required to understand the technical material covered in this monograph. In this monograph we pay homage to one of the crowning intellectual achievements of Western Civilization: The Calculus. We do so by investigating a number of historically important problems that challenged 17th and 18th century mathematicians and physicists. Each problem solution leverages the unique and powerful analytic ability of calculus to model phenomena involving rates of change.

This monograph is the third in a series devoted to special topics in Mathematics; in particular those topics not covered in a standard High School mathematics core curriculum. As such, the target audience would be mathematically motivated and/or intellectually curious High School students and recreational mathematicians. No mathematics beyond Introductory Calculus is required to understand the technical material covered in this monograph. The first monograph - A Finite Introduction To Infinity - explores transfinite arithmetic and set theory, the infinite levels of infinity, and the paradoxical nature of infinite sets, leading up to the famous Banach-Tarski Paradox. The second monograph - Counting With Intent - explores advanced counting techniques: combinatorics (eg, poker hand evaluations), Markov analysis (a tennis match analysis), discrete sequence summation (eg, Fibonacci series), and Stochastic analysis (Queueing Theory). In this monograph we pay homage to one of the crowning intellectual achievements of Western Civilization: The Calculus. We do so by investigating a number of historically important problems that challenged 17th and 18th century mathematicians and physicists. Each problem solution leverages the unique and powerful analytic ability of calculus to model phenomena involving rates of change.

I have a Masters Degree in Mathematics from UMass-Amherst. I worked for 18 years at AT&T Bell Laboratories working in a variety of applied research and product development organizations. My post-AT&T years were spent working with numerous high-tech start-ups and enterprises (e.g., Cisco, EMC, Schneider-Electric, American Medical Devices) developing a diverse range of software based products and solutions across multiple technology domains ranging from Network Management, Cyber Security, Building Systems, and remote Tele-Medicine. I currently find myself happily retired and reacquainting myself with my first love: Mathematics.