Given a tangent with point of contact and the directrix, to construct the parabola.

Given the axis, focus, and one tangent, to construct the parabola.

Construct an animation displaying all possible parabolas tangent to a fixed circle having a fixed diameter as the axis.

Given the directrix and two points, to construct the parablas passing through the points.

Given 2 tangents and directrix, to construct the parabola.

Let a,
b, c, d be given. Construct the graph of the function

((ax+b)x+c)x+d

Let a, b, c, d, e be given. Construct the graph of the function

Given
k, a, b, c, d, construct the graphs of

k(x-a)(x-b),

k(x-a)(x-b)(x-c),

k(x-a)(x-b)(x-c)(x-d).

Given
four points (x_{1},y_{1}), (x_{2},y_{2}), (x_{3},y_{3}),
(x_{4},y_{4}), construct the graph of the cubic polynomial p
satisfying

p(x_{1})
= y_{1}

p(x_{2}) = y_{2}

p(x_{3}) = y_{3}

p(x_{4}) = y_{4}

Construct the cardioid.

Construct the nephroid

Construct the deltoid.

Construct the astroid.

Construct the part of the tangent of the astroid intercepted by the curve

Two persons walk at constant speed around
a circle. The ratio of their angular velocity is k ( k is not 0, 1 or -1). Find
the envelope of all the straight lines joining them for k = 2, 3, -2, -3. Find
the point of tangency

Construct
the double generation of the deltoid.

Construct
the double generation of the astroid

Construct
the double generation of the cardioid.

Construct
the double generation of the nephroid.

Construct
the double generation of the rose curve of three leaves.

Construct
the osculating circle of the astroid.

Construct
the osculating circle of the cardioid.

Construct
the osculating circle of the rose curve of three leaves.

Construct
two mutually orthogonal tangents of the deltoid. Where do they meet?

Construct
two mutually orthogonal normals of the deltoid. Where do they meet?

Construct
a deltoid tangent to the sides of a given triangle.

Construct
an animation displaying a deltoid sliding along two orthogonal straight lines.

Given a
fixed deltoid, construct an animation displaying its circumscribed nephroid.

Given a
fixed nephroid, construct an animation displaying its inscribed deltoid

Construct two identical cardioids each rotating about
its cusp meeting orthogonally on the line segment joining the cusps.

Let AB be a fixed diameter of a circle O. Through a
variable point C on O construct two cardioids with AB and BC as tangents and
with the cusps at the distance of 2AB apart.

Construct an animation displaying two
nephroids meeting orthogonally on a circle.

Construct
the tooth-wheel coupling between the deltoid and the nephroid.

Construct
the tooth-wheel coupling between the deltoid and the cardioid.

Construct
the tooth-wheel coupling between the deltoid and the 4-cusped epicycloid.

Construct
the tooth-wheel coupling between the deltoid and the 3-cusped epicycloid.

Construct
the tooth-wheel coupling between the trochoids.

Construct
the lemniscate with a linkage different from the previous one.

Demonstrate
how the lemniscate can be drawn with the crossed parallelogram.

Demonstrate
how the lemniscate can be drawn with the crossed parallelogram.

Construct
two circles of the same radius with each rotating about a point not located at
the center while remaining tangent to each other.

Construct
two identical ellipses with each rotating about one of its two foci while
remaining tangent to each other.

Design
a linkage to draw the ellipse.

Demonstrate
how the lemniscate can be drawn with the crossed parallelogram.

Construct
Peaucellier's linkage converting straight line motion to circular motion.

Design
a linkage to draw the cardioid.

Illustrate
Pascal's Mystic Hexagram Theorem for a Circle: The points 12,

23, 31 of the intersection of the three pairs of opposite
sides 1'2 and 12', 2'3

and 23', 3'1 and 13' of a hexagon 12'31'23' inscribed in a
circle lie on a line.

Construct
the conic passing through five given points.

Construct
the conic passing through four given points and tangent to a given

line which contains one of the points.

Given
three points and two lines each containing one of the points,

construct the conic passing through the three points and
tangent to the lines

at the given points.

Illustrate
Brianchon's Theorem for a Circle: If a hexagon is circumscribed

about a circle, the three joining pairs of opposite vertices
are concurrent.

Construct
the conic tangent to five given lines.

Construct
the conic tangent to four given lines and passes through a point on

one of them.

Construct
the conic tangent to three given lines and passes through two

points on two of them.

Construct
a script which constructs the inversion of a circle given its center and a
point on the circumference.

Construct an animation making the chain of
circles move about the center.

Construct
an animation illustrating Steiner's Porism: For any two (nonconcentric) circles
one inside another, if circles are drawn successively touching them and one
another so the last one touches the first, then it will always happen whatever
the position of the first circle.

Investigate
the various properties in the configuration of Steiner's porism for the chain
of three circles.

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Construct
the Poncelet's Porism in Poincare's Model.

Decompose
an equilateral triangle into four pieces and reassemble them into a square.

Given
two acute triangles S and T, show that each can be decomposed into three pieces

S =
S_{1} U S_{2} U S_{3}

T = T_{1} U T_{2} U T_{3}

so that
S_{i} is similar to T_{i} for i = 1,2,3.

Construct
a linkage to draw the lemniscate after this design:

I.M.
Yaglom, Geometric Transformation III, p. 15. Is there anything wrong?

This
configuration was found in the Japanese temple. Make a dynamic animation out of
it.

Construct
the figure illustrating Morley's Theorem.

Explore
the concurrent property in Morley's Theorem.

The
similar concurrent property holds for the exterior case of Morley's Theorem.

What
properties can be seen from this figure?