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# Constructions

Straightedge compass construction, also known as ruler – compass constructions or classical constructions are assumed to be infinite in length. It has an idealized ruler known from its straightness, and can only use the idealizing ruler compass. The idealized ruler is known for its straight edges and has its construction as a classic construct.
It is assumed that the compass has a maximum and minimum radius and may not be used directly to transmit the distance. Also, it could not even be used to mark a route on the compass by adjusting it and then walking along it. It was assumed that the compass collapses when drawn in a circle, but it can collapse when lifted from the side, as in the case of the circle – drawing compass.
Greek geometric construction that contains all the elements of Euclid. This construction is known as the Euclidean construction. Such constructions are at the center of many of the most important mathematical and mathematical concepts in the history of mathematics.
The Greeks formulated much of what we consider geometry more than 2000 years ago, but they were unable to solve the problem. The mathematician Euclid documented this in his book “Elements,” which is still regarded as an authoritative reference for geometry. It was not until hundreds of years later that the constraints imposed actually made the problems impossible.
Building techniques became part of geometry as a subject, and in my work I have used them extensively in the construction of many of the most important buildings in the world, such as the World Trade Center and the Statue of Liberty in New York.
It also provides insights into geometric concepts and gives us the ability to draw things when direct measurement is not appropriate. It is also a more powerful conical drawing tool, as we can construct complex numbers that do not have a solid construction. For example, it is not possible to construct a regular 23-gon or 29-gon with these tools, but you cannot solve it without using neurosis constructions.
It is still open whether normal 25-gon or 31-rackets are constructable with these tools, but they are bebe constructable with them.
Given the problem of finding the center of a line, it is very difficult to measure the obvious line and divide it by two. The algorithm involves a repeated doubling of the angle and becomes physically unusable after about 20 binary digits.
There is definitely not enough room in a graduated ruler to draw a straight line, even with the most powerful ruler in the world.
Euclid and the Greeks solved this problem by drawing shapes using arithmetic and using compasses and conical drawing tools. A fold corresponding to the Huzita Hatori axioms can be constructed with a compass and a cone drawing tool. For example, it would allow us to take three lines with a distance of one third of the length of a straight line and draw a line that runs through a particular segment and cuts through all three lines so that the distance between the intersections corresponds to the given point.
The Greeks called this neusis (inclination) or tendency (inclination) because the new line tends to this point. Squaring a circle (also known as squaring the circle) involves constructing a square in the same area as the given circle, using only a straight line and a compa. This proved impossible because squaring produces transcendental numbers, i.e. the number of squares in a given area and not the total area of that area.
Only certain algebraic numbers can be constructed with a ruler and compass alone, like integers constructed from a square root. Complex numbers, including the extraction of cube roots, have solid constructions, but complex numbers, expressed only by the field operation of square roots, have a planar construction.
Complex numbers with solid constructions lie in a field extension bordered by a tower, where the extension has grades 2 and 3. They have a flat construction in the shape of a square root with degrees 1, 2, 3, 4 and 5.
We try to reduce the total number of operations (called simplicity) required for a geometric construction. It turns out that any construction that is possible with a compass or a straight line can be done by considering how to construct a line when its two endpoints are located. We reduce geometric designs to five operating modes and reduce them to a total of five. Each point has a solid construction and is constructed with a possibly hypothetical conical drawing tool that pulls the cones from an already constructed focus.
Ramanujan (1913 – 1914) and Olds (1963) give geometric constructions a number of different operating modes, each with its own set of operations and operating modes.
In 1837, Pierre Wantzel proved impossible to apply mathematical theory in this field by using the mathematical theories of the field. A number can be constructed if and only if it can be written with a number of different operations, such as the length of a line or the angle between two lines. The angle of cosine is a constructable number, but it is not constructable, like every angle except cosine. Only if a length represents a constructable number, can it be constructable, and only for any length.