trisect$85236$ - translation to ελληνικό
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trisect$85236$ - translation to ελληνικό

CONSTRUCTION OF AN ANGLE EQUAL TO ONE THIRD A GIVEN ANGLE
Trisecting the angle; Trisection of an angle; Trisection of the angle; Trisecting an angle; Trisecting angles; Trisection; Trisection of angle; Trisection of any angle; Trisecting an arbitrary angle; Trisections of an angle; Trisect every angle; Trisect any angle; Trisect an angle; Trisect angles; Trisect an arbitrary angle; Trisected angle; Angle trisector; Trisect; Trisecting the Angle; Trisect the angle
  • Bieberbach's trisection of an angle (in blue) by means of a right triangular ruler (in red)
  • p. 186}}
  • left
  • Sylvester's Link Fan
  • A tomahawk trisecting an angle. The tomahawk is formed by the thick lines and the shaded semicircle.
  • Trisection of the angle using marked ruler
  • left

trisect      
v. τριχοτομώ, διαιρώ εις τρία

Ορισμός

Trisection
·noun The division of a thing into three parts, Specifically: (Geom.) the division of an angle into three equal parts.

Βικιπαίδεια

Angle trisection

Angle trisection is a classical problem of straightedge and compass construction of ancient Greek mathematics. It concerns construction of an angle equal to one third of a given arbitrary angle, using only two tools: an unmarked straightedge and a compass.

In 1837, Pierre Wantzel proved that the problem, as stated, is impossible to solve for arbitrary angles. However, some special angles can be trisected: for example, it is trivial to trisect a right angle (that is, to construct an angle of 30 degrees).

It is possible to trisect an arbitrary angle by using tools other than straightedge and compass. For example, neusis construction, also known to ancient Greeks, involves simultaneous sliding and rotation of a marked straightedge, which cannot be achieved with the original tools. Other techniques were developed by mathematicians over the centuries.

Because it is defined in simple terms, but complex to prove unsolvable, the problem of angle trisection is a frequent subject of pseudomathematical attempts at solution by naive enthusiasts. These "solutions" often involve mistaken interpretations of the rules, or are simply incorrect.