Search Results for “fermat-point”
Chord Angle Theorem
The chord angle theorem states that in an inscribed triangle (ABC) where A is the center of the circle and BC is a chord, and BDC is an inscribed triangle on the same chord, angle BDC must equal one half of angle BAC. Try changing the angle and moving point D and observe the theorem’s truth. Note: the measure of angle BDC is being constantly recalculated as point D is dragged, but it doesn't change because of this theorem.
Exploring Rolle's Theorem
Explore conditions of the Rolle's Theorem. The applet shows the graph of continuous differentiable function f(x) on a closed interval [a, b]. Case 1. f(x) < f(a) for some x inside the interval (a, b). Can you find the number c such that f'(c)=0? What did you notice about the point when f'(c)=0? Case 2. f(x) > f(a) for some x inside the interval (a, b). Can you find the number c such that f'(c)=0? What did you notice about the point when f'(c)=0? Can a given function have more than one number on a given interval such that f'(c)=0?
Parabola Polar Line
The locus of the intersection of tangents at the ends of chords of a parabola through a given fixed point is a straight line. This is called the polar line of the given point
Sliding Ladder Problem
One of the first calculus class problems is the sliding ladder. In this problem, a ladder is resting against a wall when, all of a sudden, it starts sliding down! In this problem you're solving for dx/dt or the rate at which the point B is moving away from the wall (point C). Input constraints: -The rate of slide must be negative for the ladder to slide down -The initial height of the ladder must be less than the ladders length
Pedal Triangles
The loci of the midpoints of the sides of pedal triangles form ellipses as the pedal point moves around a circle.
circle intersections
Can you conjecture a formula for the product of the two distances from a point to a circle?
Spin the Chrome Icon!
This close replica of the logo/icon for Google Chrome, the world's most popular web browser, is built off of a geometric reconstruction of the logo's shape, allowing the logo to "spin" as you drag a point around its edge.
And the envelope please...
What is the phantom curve you see when you look at a set of lines, perpendicular to a set of chords through a common point in a circle?
