Circle | Wikipedia audio article
This is an audio version of the Wikipedia Article:
https://en.wikipedia.org/wiki/Circle
00:01:12 1 Euclid's definition
00:01:37 2 Terminology
00:04:32 3 History
00:06:39 4 Analytic results
00:06:49 4.1 Length of circumference
00:07:36 4.2 Area enclosed
00:09:19 4.3 Equations
00:09:27 4.3.1 Cartesian coordinates
00:18:02 4.3.2 Polar coordinates
00:19:35 4.3.3 Complex plane
00:21:09 4.4 Tangent lines
00:23:51 5 Properties
00:24:08 5.1 Chord
00:27:54 5.2 Tangent
00:29:19 5.3 Theorems
00:31:44 5.4 Inscribed angles
00:32:34 5.5 Sagitta
00:32:39 6 Compass and straightedge constructions
00:32:48 6.1 Construct a circle with a given diameter
00:34:53 6.2 Construct a circle through 3 noncollinear points
00:35:30 7 Circle of Apollonius
00:36:59 7.1 Cross-ratios
00:37:07 7.2 Generalised circles
00:37:41 8 Circles inscribed in or circumscribed about other figures
00:38:04 9 Circle as limiting case of other figures
00:38:47 10 Circles in other p-norms
00:40:48 11 Squaring the circle
00:41:45 12 See also
00:42:47 12.1 Specially named circles
00:44:08 12.1.1 Of a triangle
00:45:26 12.1.2 Of certain quadrilaterals
00:46:15 12.1.3 Of certain polygons
00:50:04 12.1.4 Of a conic section
Listening is a more natural way of learning, when compared to reading. Written language only began at around 3200 BC, but spoken language has existed long ago.
Learning by listening is a great way to:
increases imagination and understanding
improves your listening skills
improves your own spoken accent
learn while on the move
reduce eye strain
Now learn the vast amount of general knowledge available on Wikipedia through audio (audio article). You could even learn subconsciously by playing the audio while you are sleeping! If you are planning to listen a lot, you could try using a bone conduction headphone, or a standard speaker instead of an earphone.
Listen on Google Assistant through Extra Audio:
https://assistant.google.com/services...
Other Wikipedia audio articles at:
https://www.youtube.com/results?searc...
Upload your own Wikipedia articles through:
https://github.com/nodef/wikipedia-tts
Speaking Rate: 0.8774763795835954
Voice name: en-US-Wavenet-E
"I cannot teach anybody anything, I can only make them think."
Socrates
SUMMARY
=======
A circle is a simple closed shape. It is the set of all points in a plane that are at a given distance from a given point, the centre; equivalently it is the curve traced out by a point that moves so that its distance from a given point is constant. The distance between any of the points and the centre is called the radius. This article is about circles in Euclidean geometry, and, in particular, the Euclidean plane, except where otherwise noted.
A circle is a simple closed curve that divides the plane into two regions: an interior and an exterior. In everyday use, the term "circle" may be used interchangeably to refer to either the boundary of the figure, or to the whole figure including its interior; in strict technical usage, the circle is only the boundary and the whole figure is called a disc.
A circle may also be defined as a special kind of ellipse in which the two foci are coincident and the eccentricity is 0, or the two-dimensional shape enclosing the most area per unit perimeter squared, using calculus of variations.