When Does a Line Become a Shape?

When Does a Line Become a Shape? — page 3 — EUCLID'S BUILDING BLOCKS GEOMETRY IS THE MATHEMATICS OF MEASURING THE EARTH More than 2,000 years ago the ancient Greeks looked at the shapes in the world around them and want ed to systematically capture what they saw One of the first math ematicians to do this in a formal way was Euclid of Alexandria He discussed his own ideas and those of mathematicians before him in 13 books called Euclid’s Elements These books formed the basis of geometry and many of Euclid’s ideas are still taught in classrooms today Euclid centered his work on five postulates or statements that are believed to be true without requiring proof Over the years the truth of the fifth postulate has been questioned However the geometry you learn accepts the fifth postulate to be true just as Euclid did Euclid also had five common notions that he believed to be true for numbers as well as shapes With only these 10 axioms or basic assumptions Euclid was able to create 465 new ideas about geometry You still learn about Euclid’s ideas today and honor EMPHASIZES HIS SCHOLARLY PURSUITS A 17TH-CENTURY PAINTING OF EUCLID 6

When Does a Line Become a Shape? — page 4

When Does a Line Become a Shape? — page 5 — his work by calling the subject Euclidean geometry Euclid started his study of geometry with two basic shapes the most basic shapes that you know the line and the circle According to Euclid all other shapes can be constructed using only these two A line is the sim plest of shapes defined as a straight path that goes on forever One idea that is commonly studied in geometry is how lines interact 8

When Does a Line Become a Shape? — page 6 — INTERSECTING LINES ARE FOUND EVERYWHERE TATION MAPS ESPECIALLY IN TRANSPOR with or relate to each other Some lines are parallel to one another meaning they never cross each other Where have you seen lines that look like this How about railroad tracks Do you know for sure they will never cross To be certain mathematicians can use a cou ple of different methods or tests They may test to make sure that the lines are always the same distance apart In the United States with the building of the Transcontinental Railroad the government set the width of the tracks at 4 feet 8 5 inches Such a uniform width ensured that the tracks could never get closer together Another method of determining parallel lines involves the use of per pendicular lines Lines that are perpendicular intersect at 90-degree an gles Two perpendicular lines resemble a plus sign or a lowercase t Where have you seen perpendicular lines Think back to those railroad tracks from earlier Between the two pieces of track there are other pieces connect ing them called ties If the tie is placed between the two pieces of track so that it is perpendicular to both of them then the tracks are parallel And if every tie on the length of the track is perpendicular the tracks will always be parallel Geometry is about so much more than lines though It’s tough to con struct shapes with just lines alone especially if lines are supposed to go on TWO PERPENDICULAR LINES RESEMBLE A PLUS SIGN t OR A LOWERCASE 9

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