Construction
The circle of Apollonius through vertex of triangle may be constructed by finding the two (interior and exterior) angle bisectors of the two angles formed by lines and at vertex, and intersecting these bisector lines with line . The line segment between these two intersection points is the diameter of the circle of Apollonius. The isodynamic points may be found by constructing two of these circles and finding their two intersection points.
Another compass and straight-edge construction involves finding the reflection of vertex across line (the intersection of circles centered at and through ), and constructing an equilateral triangle inwards on side of the triangle (the apex of this triangle is the intersection of two circles having as their radius). The line crosses the similarly constructed lines and at the first isodynamic point. The second isodynamic point may be constructed similarly but with the equilateral triangles erected outwards rather than inwards.
Alternatively, the position of the first isodynamic point may be calculated from its trilinear coordinates, which are
The second isodynamic point uses trilinear coordinates with a similar formula involving in place of .
Read more about this topic: Isodynamic Point
Famous quotes containing the word construction:
“There’s no art
To find the mind’s construction in the face.”
—William Shakespeare (1564–1616)
“There is, I think, no point in the philosophy of progressive education which is sounder than its emphasis upon the importance of the participation of the learner in the formation of the purposes which direct his activities in the learning process, just as there is no defect in traditional education greater than its failure to secure the active cooperation of the pupil in construction of the purposes involved in his studying.”
—John Dewey (1859–1952)
“When the leaders choose to make themselves bidders at an auction of popularity, their talents, in the construction of the state, will be of no service. They will become flatterers instead of legislators; the instruments, not the guides, of the people.”
—Edmund Burke (1729–1797)