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Dissect a regular triangle into six pieces to form a regular hexagon

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Reassemble this into a circular disk

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Gear-wheels coupling formed by epicycloids	Gear-wheel coupling among the epicycloids and hypocycloids
Gear-wheel coupling among trochoids	Gear tooth coupling between an epicycloid and a hypocycloid
Deltoid-cardioid coupling	Nephroid-cardioid coupling
Nephroid-epicycloid 4 coupling
Rotating rose curve	r = cos 7t/2 + cos s
Bowditch curve	Trammel of Archimedes
Process of constructing the graph of a polynomial with coefficients given	Process of constructing the graph of a polynomial with roots given
Proof of Pythagoras theorem with the least number of dissections	Linkage to generate an ellipse
Hart's Linkage	Linkage to generate a pear-shaped curve
Linkage to generate the lemniscate of Bernoulli (1)	Linkage to generate the lemniscate of Bernoulli (2)
Two rotating ellipses sliding against each other	Break Dancing
Linkage to generate the nephroid	Linkage to generate the cardioid
Triangle sliding on two orthogonal lines	Triangle sliding on two lines
Orthogonal tangents of the cardioid	Orthogonal tangents of the deltoid
Symmetrically located tangents of the astroid	This is how it's constructed
Symmetrically located tangents of the nephroid	This is how it's constructed
The cardioid sliding on two orthogonal lines	The nephroid sliding on three symmetrically located lines
Three parallel tangents to the cardioid	Deltoid sliding inside a nephroid
Pentagon inscribed in cardioid with constant area	Equal viewing angle from the cusp
Escribed pentagon with constant area
Double generation of the deltoid	Double generation of the astroid
Double generation of the cardioid	Double generation of the nephroid
Double generation of the rose curve	A property of a chain of tangential circles
Osculating circle of the deltoid	Osculating circle of the astroid
Osculating circle of the nephroid	Osculating circle of the cardioid
Osculating circle of the cycloid
Osculating circle of the ellipse	Osculating circle of the parabola
Osculating circle of the lemniscate of Bernoulli	Osculating circle of the trochoid
Osculating circle of the complex curve (1)	Osculating circle of the complex curve (2)
Osculating circle of the "egg"	Osculating circle of the spiral
Nephroid passing through the vertices of a regular triangle	Astroid passing through the vertices of a regular triangle
Caustic property of the circle	Caustic property of the cardioid
Principle behind the cardioid condensor	Simple harmonic motion related to the cardioid
Hyperbolas orthogonal to a fixed ellipse	Ellipses orthogonal to a fixed hyperbola
Rectangles circumscribed to an ellipse	Orthogonal normals to a cardioid
f(x,t)=sin(x+t)	Formation of the cycloid
Formation of the nephroid	Formation of the deltoid
Formation of the astroid	Formation of the cardioid
Formation of the ellipse
Diameter of a rolling circle	Ellipse inscribed in the astroid
Poncelet's porism between two ellipses
Ruler construction: a line through a point and parallel to a segemnt with midpoint given	Ruler construction: find the midpoint of a line segment with a parallel line given
Ruler construction: Given a circle and its center, construct an inscribed square

Locating the center of a circle using compass alone

Regular pentagon constructed with the compass alone

 

A property of the reuglar 7-gon	A property of the regular 9-gon
A property of the regular 11-gon	A property of the regular 13-gon