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Understand how to calculate a circle's area with the help of chain and ruler
Eccentricity of conic sectionsThe eccentricity of a conic section completely characterizes its shape. For example, all circles have zero eccentricity, and all parabolas have unit eccentricity; hence, all circles (and all parabolas) have the same shape, only varying in size. (Under appropriate magnification they are indistinguishable.) In contrast, ellipses and hyperbolas vary greatly in shape. transformation of a circular region into an approximately rectangular region Figure 11: Beltrami's circle model. concentric circles and infinity conic sections Projective conic sectionsThe conic sections (ellipse, parabola, and hyperbola) can be generated by projecting the circle formed by the intersection of a cone with a plane (the reality plane, or RP) perpendicular to the cone's central axis. The image of the circle is projected onto a plane (the projective plane, or PP) that is oriented at the same angle as the cutting plane (Ω) passing through the apex (“eye”) of the double cone. In this example, the orientation of Ω produces an ellipse in PP. Figure 5: Intersecting circles. If a circle with centre A has a point X inside, as well as a point Y outside, a second circle with centre B, and if X and Y lie on AB, then the circles have at least one common point on each side of AB. Chord in a circle Pascal's projective theoremThe 17th-century French mathematician Blaise Pascal proved that the three points (x, y, z) formed by intersecting the six lines that connect any six distinct points (A, B, C, D, E, F) on a circle are collinear.
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Equations written on blackboard
Numbers and Mathematics
Italian-born physicist Dr. Enrico Fermi draws a diagram at a blackboard with mathematical equations. circa 1950.
Define It: Math Terms
Discover
airplane in flight (plane, aircraft, flying)
7 Puzzling Plane Disappearances
Queen Elizabeth II addresses at opening of Parliament. (Date unknown on photo, but may be 1958, the first time the opening of Parliament was filmed.)
All 119 References in “We Didn’t Start the Fire,” Explained
The impeachment trial of Pres. Andrew Johnson, illustration from Frank Leslie's Illustrated Newspaper, March 28, 1868.
What If the President Is Impeached?
African Americans demonstrating for voting rights in front of the White House as police and others watch, March 12, 1965. One sign reads, "We demand the right to vote everywhere." Voting Rights Act, civil rights.
Timeline of the American Civil Rights Movement
Car with a pickle design in the Zagreb Red Bull Soapbox Race, Zagreb, Croatia, September 14, 2019. (games, races, sports)
10 Unusual Sports
Cleopatra hieroglyphic carving the Ancient Egyptian queen Cleopatra. Wall of the Temple of Horus at Edfu, Egypt.
What Did Cleopatra Look Like?
Time zone map with standard time zones and International Date Line
Why Are Some Time Zones 30 Minutes Off Instead of an Hour?

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Understand how to calculate a circle's area with the help of chain and ruler
Understand how to calculate a circle's area with the help of chain and rulerVisual derivation of a circle's area.
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circle, geometrical curve, one of the conic sections, consisting of the set of all points the same distance (the radius) from a given point (the centre). A line connecting any two points on a circle is called a chord, and a chord passing through the centre is called a diameter. The distance around a circle (the circumference) equals the length of a diameter multiplied by π (see pi). The area of a circle is the square of the radius multiplied by π. An arc consists of any part of a circle encompassed by an angle with its vertex at the centre (central angle). Its length is in the same proportion to the circumference as the central angle is to a full revolution.

This article was most recently revised and updated by Erik Gregersen.