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What areas can be a trap for incorrect parallelism?
Incorrect parallelism is a common problem in certain branches of mathematics, especially those involved in computing.
What are the rule of parallelism?
Be cautious of word repetition unless it is used as a tool to create impact.
Is the letter Z parallel?
Yes, because the top and bottom go the same way. The diagonal line means nothing in parallelism.
What are the conditions that guarantee parallelism?
Parallel lines are lines that are coplanar (lying on the same plane) and do not intersectwhen cut by a transversal,corresponding angles formed by line n are equal in measure,alternate interior angles are equal in measures,the measures of alternate exterior angles are equal,consecutive interior angles are supplementary,consecutive exterior angles are supplementary.
What are the titles of Euclid's Element's books?
The 13 books of Euclid's Elements are generally referred to by their book number. The main subject matter of each book: Book 1 contains the basic properties of geometry: the Pythagorean theorem, equality of angles and areas, parallelism, the sum of the angles in a triangle, and the three cases in which triangles are "equal" (have the same area). Book 2 is commonly called the "book of geometrical algebra," because the material it contains may easily be interpreted in terms of algebra. Book 3 deals with circles and their properties: inscribed angles, tangents, and the power of a point. Book 4 is concerned with inscribing and circumscribing triangles and regular polygons. Book 5 is a treatise on proportions of magnitudes. Book 6 applies proportions to geometry: Thales' theorem, similar figures. Book 7 deals strictly with elementary number theory: divisibility, prime numbers, greatest common divisor, least common multiple. Book 8 deals with proportions in number theory and geometric sequences. Book 9 applies the results of the preceding two books: the infinitude of prime numbers, the sum of a geometric series, perfect numbers. Book 10 attempts to classify incommensurable (in modern language, irrational) magnitudes by using the method of exhaustion, a precursor to integration. Book 11 generalizes the results of Books 1-6 to space: perpendicularity, parallelism, volumes of parallelepipeds. Book 12 calculates areas and volumes by using the method of exhaustion: cones, pyramids, cylinders, and the sphere. Book 13 generalizes Book 4 to space: golden section, the five regular (or Platonic) solids inscribed in a sphere.
