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Trisecting any angle

Doubling a cube

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15y ago

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What Greek constructions were never accomplished with only a straightedge and a compass?

Doubling a cube and trisecting any angle


What constructions were never accomplished by the Greeks with only a straightedge and a compass?

doubling a cube and trisecting any angle


What did the Greeks use in geometric constructions?

A straightedge and compass.


Which of these constructions is impossible using only a compass and straightedge-?

Constructions that are impossible using only a compass and straightedge include Trisecting an angle Squaring a circle Doubling a cube


What tools did the greek use in geometric constructions?

A straightedge and compass.


Many of the same constructions the Greeks performed only with straightedge and compass can be done using only a straightedge and tracing paper?

True


Which constructions is impossible using only a compass and straightedge?

doubling the cube


What tools are necessary when doing geometric constructions?

When performing geometric constructions, the essential tools are a compass, a straightedge (ruler without markings), and a pencil. The compass is used to draw circles and arcs, while the straightedge helps create straight lines between points. These tools allow for precise constructions based on classical geometric principles without relying on measurements. Additionally, paper is needed to carry out the constructions.


What tools did the Greeks use in their formal geometric constructions?

ruler tracing paper those are the wrong answers its Straightedge & Compass


What constuctions were never accomplished by the Greeks with only a straightedge and a compass?

A. Trisecting any angle B. Doubling a cube


It is not possible to trisect any angle using only a compass and straightedge.?

The impossibility of trisecting an arbitrary angle using only a compass and straightedge is a result of the limitations imposed by classical geometric constructions. This conclusion is rooted in the field of abstract algebra, specifically the properties of constructible numbers and the fact that the angle trisection leads to solving cubic equations, which cannot be accomplished with just these tools. While certain specific angles can be trisected, there is no general method for all angles. This was proven in the 19th century as part of the broader exploration of geometric constructions.


Which of the following are the tools which allowed the Greeks to exploit the five basic postulates of Euclidian geometry?

Straightedge Compass