Geometric Construction 5

Show how the deltoid is formed.

1.gif (10494 bytes)

Show how the astroid is formed.

2-1.gif (10954 bytes)

Show how the cardioid is formed.

3.gif (8063 bytes)

Show how the nephroid is formed.

4.gif (8804 bytes)

@

Construct the deltoid as the envelope of its tangent.

5.gif (9469 bytes)

Construct the astroid as the envelope of its tangent.

6.gif (14444 bytes)

Construct the cardioid as the envelope of its tangent.

7.gif (10660 bytes)

Construct the nephroid as the envelope of its tangent.

8.gif (13058 bytes)

@

Show how the deltoid may be generated in two ways.

9.gif (13096 bytes)

Show how the cardioid may be generated in two ways.

10.gif (14093 bytes)

Show how the astroid may be generated in two ways.

11.gif (15319 bytes)

Show how the nephroid may be generated in two ways.

12.gif (12617 bytes)

@

Construct circles enveloping both the deltoid and the 3-cusped epicycloid.

13.gif (34334 bytes)

Construct circles enveloping both the astroid and the 4-cusped epicycloid.

14.gif (33775 bytes)

@

Construct the osculating circle of the astroid.

16.gif (11823 bytes)

16-1.gif (23681 bytes)

Construct the osculating circle of the deltoid.

17.gif (9226 bytes)

17-1.gif (15661 bytes)

Construct the osculating circle of the cardioid.

18.gif (9394 bytes)

18-1.gif (31272 bytes)

Construct the osculating circle of the nephroid.

19.gif (8951 bytes)

19-1.gif (22797 bytes)