Octagon - Construction and Elementary Properties

Construction and Elementary Properties

A regular octagon may be constructed as follows:

  1. Draw a circle and a diameter AOB, where O is the center and A,B are points on the circumference.
  2. Draw another diameter COD, perpendicular to AOB.
  3. (Note in passing that A,B,C,D are vertices of a square).
  4. Draw the bisectors of the right angles AOC and BOC, making two more diameters EOF and GOH.
  5. A,B,C,D,E,F,G,H are the vertices of the octagon.

Each side of a regular octagon subtends half a right angle at the centre of the circle which connects its vertices. Its area can thus be computed as the sum of 8 isosceles triangles, leading to the result: Area = 2*a*a*(sqrt(2) + 1) for an octagon of side a.

Read more about this topic:  Octagon

Famous quotes containing the words construction, elementary and/or properties:

    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 Devil quotes Scriptures, it’s not, really, to deceive, but simply that the masses are so ignorant of theology that somebody has to teach them the elementary texts before he can seduce them.
    Paul Goodman (1911–1972)

    The reason why men enter into society, is the preservation of their property; and the end why they choose and authorize a legislative, is, that there may be laws made, and rules set, as guards and fences to the properties of all the members of the society: to limit the power, and moderate the dominion, of every part and member of the society.
    John Locke (1632–1704)