Dr. Moretti’s Mathematica Notebooks – Geometry
Mathematica Notebooks for Geometry
Important Note: The links for the notebooks open a new window or tab with a Google Drive page – the current settings for our homepages won’t allow me to host mathematica notebooks locally.
This notebook lets you explore different notions of the center of a triangle – the centroid, circumcenter, and so on.
This notebook lets you graph an affine curve and find the “points at infinity” that correspond to the projective completion (and their multiplicity).
Circles Tangent to 3 Lines
This manipulation finds the circles which are tangent to 3 given lines. Most of the time the equations of the circles will be fairly ugly even if the equations of the lines themselves are nice (the algebra underlying the problem involves solving a system of quadratic equations).
This manipulation lets you experiment with the focus-directrix definition of a conic section. You can move the focus, the points defining the directrix, and the eccentricity of the conic.
This manipulation shows one of the original ways to estimate the constant π – by thinking of it as the area of the unit circle and then estimating the area of the circle using inscribed and circumscribed polygons. The inscribed polygon areas are always under the true are and the circumscribed polygon areas are always over – but as the number of sides of the polygon grows, both areas converge on the single value of π.