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To draw the parallel (h) to a diameter g through any given point P. Chose auxiliary point C anywhere on the straight line through B and P outside of BP. (Steiner) In the branch of mathematics known as Euclidean geometry, the Poncelet–Steiner theorem is one of several results concerning compass and straightedge constructions having additional restrictions imposed on the traditional rules.
The "straightedge" and "compass" of straightedge-and-compass constructions are idealized versions of real-world rulers and compasses. The straightedge is an infinitely long edge with no markings on it. It can only be used to draw a line segment between two points, or to extend an existing line segment.
It is possible to prove compass equivalence without the use of the straightedge. This justifies the use of "fixed compass" moves (constructing a circle of a given radius at a different location) in proofs of the Mohr–Mascheroni theorem, which states that any construction possible with straightedge and compass can be accomplished with compass alone.
Parallel rule in plastic with aluminum arms lying on a cutting mat. Parallel rulers are a drafting instrument used by navigators to draw parallel lines on charts. The tool consists of two straight edges joined by two arms which allow them to move closer or further away while always remaining parallel to each other.
An ornate 18th century iron straightedge. A straightedge or straight edge is a tool used for drawing straight lines, or checking their straightness. If it has equally spaced markings along its length, it is usually called a ruler. Straightedges are used in the automotive service and machining industry to check the flatness of machined mating ...
A parallel ruler-equipped drawing board. Drawing from an article published in a Norwegian technical journal Teknisk Ukeblad in 1893. The article dealt with a new kind of vertical drawing apparatus. The board was equipped with a lift mechanism, improving the ergonomy when doing large drawings.
The square root of 2 is equal to the length of the hypotenuse of a right triangle with legs of length 1 and is therefore a constructible number. In geometry and algebra, a real number is constructible if and only if, given a line segment of unit length, a line segment of length | | can be constructed with compass and straightedge in a finite number of steps.
The intercept theorem, also known as Thales's theorem, basic proportionality theorem or side splitter theorem, is an important theorem in elementary geometry about the ratios of various line segments that are created if two rays with a common starting point are intercepted by a pair of parallels.