![\"japanese](\"\/blog\/wp-content\/images\/2011\/04\/japanese-flag.png\")
Japanese flag <\/p>\n
Japanese flag <\/p>\n
Most people would describe the Japanese flag as being \"a red circle on a white background\". But is it really, mathematically speaking?<\/p>\n
Reader Irshad Hussain recently asked for "a clear definition of a circle.\" He wondered if the circle is only a boundry or does it include the whole interior also?<\/p>\n
When you think "circle", do you see a curve<\/strong>, like this:<\/p>\n Or do you think of it as a region<\/strong>, like this?<\/p>\n Math Open Reference<\/a> defines a circle as:<\/p>\n A line forming a closed loop, every point on which is a fixed distance from a center point.<\/p>\n<\/blockquote>\n This is the first diagram above.<\/p>\n The American Heritage Science Dictionary gives the following definition, also considering the circle as a curve, not a region:<\/p>\n A closed curve whose points are all on the same plane and at the same distance from a fixed point (the center). <\/p>\n<\/blockquote>\n Wolfram|Alpha also defines it as a plane curve<\/a>. (And that's all. Even though it lists several important equations for circles, no mention is made of the property of equidistance from a point). <\/p>\n Google's definitions cover both cases, but give precedence to the region definition (the second diagram):<\/p>\n 1. A round plane figure whose boundary (the circumference) consists of points equidistant from a fixed point (the center) Here's a definition that gives a broader view:<\/p>\n Ellipse in which the two axes are of equal length. <\/p>\n<\/blockquote>\n One of the silliest definitions is from the The American Heritage Dictionary:<\/p>\n Circle: A planar region bounded by a circle.<\/p>\n<\/blockquote>\n How can an object be bounded by itself? One could argue the definition itself is circular. \ud83d\ude42 <\/p>\n The simplest solution is to define a circle<\/strong> as a plane curve and a disk<\/strong> as a plane region, bounded by a circle. However, \"disk\" to me suggests a 3-dimensional object (a very flat cylinder).<\/p>\n What are your thoughts on how we should define a cirlce?<\/p>\n See the 7 Comments<\/a> below.<\/p>\n","protected":false},"excerpt":{"rendered":"![\"circle](\"\/blog\/wp-content\/images\/2011\/04\/circle.png\")
<\/p>\n![\"circle](\"\/blog\/wp-content\/images\/2011\/04\/circle-closed.png\")
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\n2. The line enclosing such a figure<\/p>\n<\/blockquote>\n\n
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Is the circular region a disk?<\/h2>\n