These visualization tools are part of Mike Delmonaco and William Liu's senior project. These were programmed using HTML and javascript. Javascript needs to be enabled for these to run. The goal of this project is to help teachers provide an intuition through an interactive visual medium. see the code here

# Algebra and Trig

• Complex Product

Select two complex numbers and see the product. The arcs help show how complex multiplication is a dilation and rotation (all 3 arcs have the same angle).

• Complex Sum

Select two complex numbers and see the sum. The lines help show how complex addition is a sequence of translations.

• Focus and Directrix

Select the location of the focus and directrix of a parabola and see how the parabola changes. The circle and its radii show how the focus is equidistant from the directrix on the parabola.

• Function Transformations

Select a function and apply transformations to it. See the written form and the graphed form change.

• Normal Distribution

This one isn't interactive, but simulates data being collected which follows a normal distribution.

• Unit Circle

Select an angle and which trig functions to display on the unit circle

# Calculus

• Euler Method

Select a first order differential equation, a starting point, and a dx and the approximate solution will be traced out

• Riemann Sum

Select a function, starting x-value, ending x-value, rectangle width, and sum type and it the rectangles will be shown.

• Tangent Line

Select a function and an x-value and the function and tangent line will be graphed.

• Taylor Series

Select a function, center x-value, and degree and the function and polynomial will be graphed.