# Euclid's Muse

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# Search Results for “reflections”

##### Combination of Reflections through Parallel Lines
Press Reﬂect twice. Now drag point I so the orange triangle lies over the image under the second reﬂection.  Can you describe another transformation equivalent to the two reflections?

Tags: reflections, translations, transformations

##### Combination of Reﬂections through Oblique Lines
Set the rotation angle and drag the center of rotation O so that the orange triangle sits on top of the image under the second reﬂection.  Can you describe another transformation equivalent to the two reflections?

Tags: reflections, rotations

##### pool construction
How to create a path from E to F bouncing off 3 cushions, and using reflections.

Tags: billiards, reflections

By Duncan
##### Pool reflections
We look at the path of a pool ball as it bounces off 3 cushions

Tags: reflection, transformation

By Marissa
##### Parallels and Reflections
Given triangle ABC, parallel lines DC and EA are reflected in BC and BA respectively. What is the locus of F, the intersection of the reflected lines? (This problem comes from Alex Turzillo's project entitled “Geometric Measure of Aberration in Parabolic Caustics”).

Tags: puzzlers, geometry, parallels, locus

##### Kaleidoscope
A kaleidoscope is typically made with  mirrors aligned as an equilateral triangle and rotated.  Multiple reﬂections form a symmetrical pattern which changes as the triangle is rotated. Drag the corners of the four original triangles to change the pattern, then drag the red dot to rotate the kaleidoscope.

Tags: Kaleidoscope, reflections

##### Reflection Clock
You can reﬂect the triangle in the minute hand, then reﬂect the reﬂection in the second hand.  How long does it take to do a complete rotation? You can change the triangle by dragging the red points.

Tags: clocks, reflections

##### Kaleidoscope
A kaleidoscope works by mirrors. Specifically an equilateral triangle of mirrors which present reflections and reflections of reflections.  Here is the inner core.  You can drag the red point to rotate the kaleidoscope.  You can also drag the vertices of the original triangles.

Tags: reflection, kaleidoscope

##### Maximum Perimeter Triangle
Constant force actuators push outwards.  As the potential energy in each actuator is equal to its length, this machine should settle where the triangle's perimeter is maximum. Press Show to see the reflections in the tangents of a beam of light transmitted along one edge of the triangle.

Tags: maximum, Fagnano, perimeter

##### Symmedian Point
Lets take 3 stretched springs attached to the sides of a triangle (in such a way that they can slip along the lines).  These will be ideal springs with 0 natural length.  Attach all 3 to a mass D, where will it end up? Press Show to see the geometric answer. (Grey lines are medians, purple lines are angle bisectors, and yellow lines are the reflections of the medians in the angle bisectors.) Now, can you work out why?

Tags: triangle, symmedian