# Euclid's Muse

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# Search Results for “Proportional-point”

##### Polar Proportional Point and Circle Puzzler 2
A circle is centered at the origin and its radius is defined by the distance between the origin and a point, P. P is defined by a polar function, s(t), and is located at the current value of t. Adjust t, or animate it by pressing ”go”. What is s(t)? Look at the .gx source for the answer.   Hint: if you look closely, s(t) can be seen in dark purple. It is a particular ”polar flower”.

Tags: Polar-function, proportional-point, circle, radius, flower, puzzler

##### Polar Proportional Point and Circle Puzzler 3
A circle is centered at the origin and its radius is defined by the distance between the origin and a point, P. P is defined by a polar function, u(t), and is located at the current value of t. Adjust t, or animate it by pressing ”go”. What is u(t)? Look at the .gx source for the answer. Hint: if you look closely, u(t) can be seen in dark gold. It is a particular ”polar flower”.

Tags: Polar-function, proportional-point, circle, radius, flower, puzzler

##### Polar Proportional Point and Circle Puzzler
A circle is centered at the origin and its radius is defined by the distance between the origin and a point, P. P is defined by a polar function, r(t), and is located at the current value of t. Adjust t, or animate it by pressing ”go”. What is r(t)? Look at the .gx source for the answer. Hint: if you look closely, r(t) can be seen in dark blue. It is a particular ”polar flower”.

Tags: Polar-function, proportional-point, circle, radius, flower, puzzler

##### Double Transforming Pentagons
Two pentagons are nested within a third, regular pentagon (ABCDE). They are each defined by a point on each side of ABCDE; these points are proportional along their sides at functions of t. Determine the function of t that represents the proportionality of each point. Notice that both pentagons are congruent to ABCDE when t = 0 and t = 1.

Tags: Pentagon, Proportional, Proportionality, N-gon, Puzzler

By Marissa
##### Example: Clock
From "Creating HTML5 Apps with Geometry Expressions." Download the GX file to see how this app was made.

Tags: example, timer, point-proportional, clock

##### Epic Circle Trace 3
Four points are located proportionally around a circle, according to four different functions of t. A figure connecting the four points is traced through t. What are the four functions? Look at the .gx source for the answer. Tip: press "go" to animate t at a constant rate from 0 to ∏ and back, looped.

Tags: Proportional-point, function, circle, puzzler, trace, ellipse, sometimes-quadrilateral

##### Epic Circle Trace 2
A triangle, defined by three points that are located proportionally around a circle by functions of t, is traced as t varies from 0 to 2Π. What are the functions of t, f(t), g(t), and h(t), that define the points D, E, and F, respectively? Hint: one of the functions is _(t) = t.

Tags: Trace, puzzler, circle, triangle, proportional-point, functions

##### 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

##### The point which minimizes weighted sum of distances to triangle's vertices
In the mechanical simulation, the actuator connecting point D to A exerts a constant force a, the actuator connecting D to B exerts force b, and the actuator connecting D to C exerts force c. At equilibrium, potential energy will be minimized.  The PE is proportional to a|AD|+b|BD|+c|CD| Press the hint button to see a geometric construction for this point. Under some circumstances the mass settles at one of the vertices.  Can you work out what these circumstances are?

Tags: fermat, toricelli, triangle

##### Simple Similar Triangles
Drag points A, B, and C to change the size and shape of the blue triangle, and its white counterpart that is similar (constrained by proportional SAS). Drag the Red point D to change the ratio in sizes. Observe the multitude of calculated output lengths and angles, and how they match the proportion value, proving similarity, regardless of the triangles' shapes/sizes.

Tags: Triangles, Similar, Ratios, Draggable, Outputs,