A Transformations Approach to Complex Numbers
This post, inspired by the work of Al Cuoco, uses Web Sketchpad to explore a transformations approach to complex numbers.
Author: Daniel Scher
Slope of the Sine Function, Part 2
In my previous post, I presented a non-algebraic approach to exploring the slope of the sine function. That method involved placing a secant line on the graph and then dragging the two points that defined the line as close together as possible to approximate the tangent line. By dragging, you were able to bring the...
Slope of the Sine Function, Part 1
When I reached calculus in my senior year of high school, it was clear that it sat atop a mountain that I had been ascending ever since my Algebra 1 class. Without the tools and procedures I had amassed from algebra and precalculus, I could never have performed the symbolic manipulations necessary to differentiate and...
Special Quadrilaterals and Their Diagonals
Given two segments and their midpoints, what quadrilaterals can you build using the segments as the diagonals of the quadrilateral?
The Origami-Math Connection
This post examines the connections between origami and geometry in the context of a new book written by Daniel Scher and Marc Kirschenbaum.
Hats Off to This Aperiodic Tiling
This post examines the role of social media in promoting the discovery of an aperiodic monotile.
Transformation Dances
This post presents virtual dances based on geometric transformations. As a penguin travels around a polygon, you, as a frog, must match its movements, but with the added challenge of dancing as a reflection, rotation, or dilation of the penguin’s path.
Transformation Games
This post presents an abundance of games that find their inspiration in three geometric transformations: reflection, rotation, and dilation.
Dynagraphs of Linear Functions
This post provides three interactive examples of dynagraphs–a powerful representation of functions that emphasizes the behavior and relationship of a function’s independent and dependent variables.
Generalizing the Pythagorean Theorem
In geometry, we learn that if we erect squares on the legs of a right triangle, the sum of their areas is equal to the area of the square on the triangle’s hypotenuse. This is visual way to conceptualize the Pythagorean Theorem. But now consider the image below that shows a bust of Pythagoras, scaled...