# Euclid's Muse

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# Search Results for “Line”

##### 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

Tags: parabola, polar

##### Hyperbola Polar Line
The polar line is the locus of the intersections of tangent lines at the ends of chords of teh parabola through a fixed point. Turns out to be conceptually important - not just a curiosity.

Tags: polar, conic, hyperbola

##### Polar Line
The locus of the intersections of the tangents at the end of chords of an ellipse which pass through a common point is a straight line. A bit of a mouthful, but play with the diagram and it will become clear.

Tags: locus, polar, ellipse, conic

##### Euclids Elements – Book 3 – Proposition 08
This proposition proves that line AD is longest, ED is shorter, FD is shorter than ED, and CD is even shorter.and that for any line there is only one other line with a point on the circle and a point at D that is equal. (Unless you drag it to somewhere it's not supposed to be) I like it because it’s colorful.

Tags: Euclid, Elements, Geometry, Triangle

##### Polar Point Parabola
The polar point of a line in a parabola is a common point to the chords defined by the common tangents through the points on the line. (Go to Full Screen if the green points won’t drag)

Tags: polar, parabola

##### Polar Point Ellipse
The polar point of a line in an ellipse is a common point to the chords defined by the common tangents through the points on the line. Play with it and the meaning will be clear! (Go to Full Screen if the green points won't drag)

Tags: ellipse, polar

##### Basic Derivatives
Drag the point to see how the slope of the line relates to the x value of the point at which it’s tangent to the function. Can you figure out what the function is, based on the values of the x and y coordinates? The slope of the line can also be represented in terms of x; can you figure out what this representation is? This representation is the derivative of the entire function, not just at a single point. This is called the derivative of the function, and can be notated by, for example, the derivative of F(x) = F’(x), although there are many other notations as well.

Tags: Calculus, Derivatives, Functions

##### Sinusoidal Tangent Mirrors
Look at a point on a sinusoidal curve (y=sin(x)) with a tangent line. Then, look at a point on the negative of your sinusoidal curve (y=-sin(x)) that is a mirror image of your first point. Then, notice that these mirror image points have mirror image tangent lines.

Tags:

##### watts up
Watt's linkage is used to generate approximate straight line motion in automobile suspensions. Aee how it works. (Yes I'm using an alpha copy of GX version 3.2)

##### Epic Circle Trace
A line passes intersects a circle at two points. Each point is located proportionally around the circle in terms of a given function of t. The path of the line’s movement is traced as t varies. Try changing/animating t. Can you figure out how each point is constrained, in terms of t? Look at the gx source file for the answer. Hint: look at the period of the movement, and how it changes as t changes.

Tags: Trace, puzzler, circle, proportional-points, functions