Maclaurin Trisectrix . It can be defined as the locus of the intersection points of two lines , each rotating at a uniform angular speed around separate points, so that the ratio of the rotation speeds is 1: 3 and the lines initially coincide with the line between the two points.
Summary
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- 1 Story
- 2 Definition
- 3 Construction
- 4 equations
- 5 Sources
History
This curve was studied by Colin Maclaurin ( 1698 to 1746 ) in 1742 four years before he died, to try to solve the problem of angle resection , one of the classic problems of Greek geometry . The problem of angle resection is to divide any angle into three equal parts using only the ruler and the compass .
Definition
It can be defined as the locus of the intersection points of two lines, each rotating at a uniform angular speed around separate points, so that the ratio of the rotation speeds is 1: 3 and the lines initially coincide with the line between the two points.
Building
CONSTRUCTION OF THE MACLAURIN TRISECTRIZ
- Show coordinate axes and let OR be the coordinate origin.
- Take a = 1 (or any other value).
- Draw the vertical linev that passes through point C (-2a, 0). This is the line x = -2a.
- Let B be the coordinate point (4a, 0).
- Plot the circumferenceCB with center B (4a, 0) and radius 4a.
- Let P be a point on the circumference CB.
- Draw the line OP.
- Let R be the intersection between the lines OP and the line x = -2a.
- Let M be the midpoint of the segment RP.
- The locus generated by M when P moves over the circumference CB is the MacLaurin Trisector.
Equations
- Cartesian equation:
- Polar equation:
- Parametric equations
