why 360 degrees?
See also the
Dr. Math FAQ:
segments of circles
Browse High School Conic Sections, Circles
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Selected answers to common questions:
Find the center of a circle.
Is a circle a polygon?
Volume of a tank.
Why is a circle 360 degrees?
- 1/4 Tank Dipstick Problem (from Car Talk) [12/04/2002]
The gauge on Rick's 18-wheeler is broken, so he uses a dowel to
measure the diesel in his tank, which is cylinder-shaped, 20 inches in
diameter, and sits on its side. How can he mark the dipstick to show
1/4 of a tank of fuel?
- Hands of a Clock [10/10/1997]
How many times do the hour and minute hands cross in a 12-hour period of
- One Circle Revolving Around Another [05/26/1999]
How many revolutions will a smaller circle make while rotating around the
perimeter of a larger circle?
- Accuracy in Measurement [02/08/2002]
Since pi is irrational, either the circumference or the diameter of a
circle must be irrational. How is that possible?
- Accurate Drawing of an Ellipse [02/14/1999]
Draw an ellipse accurately using simple tools.
- Algebraic Spirals [5/19/1995]
I have read about "algebraic" spirals called "cissoid" and "conchoid," which Descartes deemed more exact than the "transcendental" logarithmic and Archimedean spirals, but I have not been able to find any other information on these figures.
- Analytic Geometry [08/31/1997]
How do I find the standard equations of the circles that pass through
(2,3) and are tangent to both the lines 3x - 4y = -1 and 4x + 3y = 7?
- Analytic Proof that Midpoints Form a Circle [03/10/1998]
Analytic proof that midpoints between a point within a circle and its
circumference form a circle.
- Angle Inscribed in a Semicircle [11/07/2001]
Prove that any angle inscribed in a semicircle is a right angle.
- Angle Measurements of Triangles inside Semicircle [11/26/1998]
If the area of a triangle inside a semicircle is equal to the area
outside the triangle within the semicircle, then find the values of the
acute angles in the triangle.
- Another Grazing Cow [6/7/1995]
A man has a barn that is 20 ft by 10 ft. He tethers a cow to one corner
of the outside of the barn using a 50-ft rope. What is the total area
that the cow is capable of grazing?
- Applications of Parabolas [10/24/2000]
How are parabolas used in real life?
- Approximating Pi using Geometry [08/12/1998]
I need to know a simple method to find the approximate value of pi using
- Arbelos Construction [03/10/2000]
Is there a Euclidean construction for the circles that are sandwiched in
- Arc Formulas [05/08/2003]
I am trying to determine the angle of an arc from the radius and arc
length. The radius is 630 and the arc length is 66.82.
- Archimedes and the Area of a Circle [09/17/1997]
How do you find the area of a circle without pi?
- Archimedes' Method of Estimating Pi [5/29/1996]
What was Archimedes' method for estimating pi using inscribed and
circumscribed polygons about a circle?
- Arcs Inside a Square [07/25/1999]
What is the area of the figure created by the intersection of two arcs
drawn in a square of sidelength 5 units?
- Area and Perimeter in Polygons [06/24/1999]
How can I prove the formula A = (a^2n)/(4tan(180/n)) for computing the
area of a regular n-gon with sidelength a? How does this compare to the
area of a circle?
- Area, Angle of Chords of a Circle [7/25/1996]
Calculate the angles PAB and POB, the area of the sector bounded by OP,
OB and the minor arc PB.
- Are Angles Dimensionless? [08/31/2003]
If you look at the dimensions in the equation arc length = r*theta, it
appears that angles must be dimensionless. But this can't be right.
Or can it?
- Area of a Circle Segment [04/18/1999]
What are the steps for figuring out the area of a segment of a circle?
- Area of a Circle with Radius less than 1 [02/18/2002]
If the radius is less than 1 it just gets smaller and you get a smaller
- Area of a Crescent [11/10/2000]
What is the formula for the area of a crescent?
- Area of a Curved Figure [07/26/1997]
How can you find the area of a curved figure without using calculus?
- Area of an Annulus [10/13/2001]
How can I find the area of an annulus?
- Area of an Ellipse [08/18/1999]
How do you calculate the area of an ellipse?
- Area of an Ellipse Cut by a Chord [05/26/2000]
How can you calculate area of the part of an ellipse cut off by a chord,
if you know the major and minor axes, and the chord?
- Area of an Ellipse using Integral Calculus [11/4/1996]
How do you find the area of an ellipse?
- Area of an Ellipse without using Calculus [11/28/1997]
How do you find the area of an oval without using calculus?
- Area of an Oval [11/30/2001]
How do I figure out the area of an oval 17" x 38"?
- Area of a Parabola [09/05/1997]
How do you find the area of a parabola? (I just finished Algebra 2.)
- Area of A Sector of An Ellipse [02/28/1998]
Finding the area of a sector of an ellipse, given the semiminor and major
axes and the angles of the 2 vectors bounding the sector.
- Area of a Segment from Arc and Chord Length [11/27/2000]
How do you find the area of a segment of a circle if you know only the
arc length and chord length?
- The Area of a Square Inscribed in a Circle [12/23/1995]
What is the area of a square inscribed in a circle whose circumference is
- Area of Inscribed Circle [12/01/1998]
Find the area of the circle inscribed in a triangle ABC using Heron's
- Area of Intersection of Two Circles [12/1/1995]
My teenage son asked me for the formula for the area of intersection of
two arbitrary circles.
- Area of Part of an Ellipse [04/07/2001]
Given an ellipse with a line bisecting it perpendicular to either the
major or minor axis of the ellipse, what is the formula for the area of
the ellipse either above or below that line?
- Area of Union of Two Circles [6/10/1996]
If the effective length of a rope tied to a goat is L, and the goat can
eat exactly half of the grass in a field, express L in terms of R.
- Areas of N-Sided Regular Polygon and Circle [02/24/2005]
The area of an n-sided regular polygon approaches the area of a circle
as n gets very large.