## MATH-ART-TECHNOLOGY Connection "An Innovative Approach to Graphing of Functions"

This course is expected to run but has not yet been scheduled.

### Course Description

The objective of this course is to provide students an in-depth understanding of mathematical functions and inequalities by producing artistic pictures and animations using the Desmos calculator (https://www.desmos.com). By graphing functions and inequalities using the Desmos calculator, students can create beautiful and interesting artistic images by drawing curves and shading various regions in different colors. Some of these creations can then be made more dynamic by animating the objects in them. Thus they will understand these rather complex equations in a playful and creative manner and in the process reinforce the concepts learned in Algebra 1 and 2.

The outline of the course is as follows:
Day 1: The students will start with various different functions (algebraic, piecewise, and sine and cosine functions), and then analyze the equations of a circle, parabola and ellipse as well as polar equations. Students will use animations to graph more complex functions.
Day 2: Students will shade regions defined by systems of inequalities using the Desmos calculator. They will then discuss parametric equations and understand how these can result in the creation of further more beautiful animations.
Day 3: Students will work in groups to create an animated picture of a cup filled with steaming coffee. They will also create art work containing flowers and some other pictures provided to them.
Days 4 & 5: Students, divided into groups of two, will select a straight forward work of art and as their final project recreate the piece of art work. Each group will analyze which mathematical functions and inequalities with which domain restrictions will be needed to replicate the art work.

After the completion of this course students will be able to: (1) identify the equation of a graph, (2) sketch the graph of various functions, (3) learn about equations of conics and how their graphs are traced by animations , (4) use translations and dilations to obtain graphs of functions from standard forms, (5) understand the connection between shaded regions and inequalities, (6) use the Desmos calculator proficiently to create graphs and animations, and (7) appreciate an innovative application of mathematics. Intimate familiarity with graphs of functions is a very important element in the content of college algebra, pre-calculus, and calculus sequence courses.

The prerequisites include some familiarity with Algebra 2 and high school Geometry.