Archimedes of Syracuse
A brilliant ancient Greek mathematician, physicist, engineer, inventor, and astronomer, known for his work on buoyancy and levers.
Quotes by Archimedes of Syracuse
The area of an ellipse is equal to the area of a circle whose radius is the geometric mean of the semi-major and semi-minor axes.
The volume of a paraboloid of revolution is half the volume of the circumscribed cylinder.
The volume of a hyperboloid of revolution is equal to the volume of a cone whose base is the same as the hyperboloid's base and whose height is the same as the hyperboloid's height, plus the volume of a cylinder whose base is the same as the hyperboloid's base and whose height is half the hyperboloid's height.
The volume of an ellipsoid of revolution is two-thirds the volume of the circumscribed cylinder.
The area of a segment of a hyperbola is equal to the area of a triangle with the same base and height, plus the area of a rectangle whose sides are the base and the difference between the height and the height of the triangle.
The area of a segment of an ellipse is equal to the area of a triangle with the same base and height, plus the area of a rectangle whose sides are the base and the difference between the height and the height of the triangle.
The center of gravity of any segment of a parabola is on its axis, at a distance from its base equal to three-fifths of the axis.
The center of gravity of any segment of a sphere is on its axis, at a distance from its base equal to the sum of the radius of the sphere and the height of the segment, divided by two.
The center of gravity of any segment of a cone is on its axis, at a distance from its base equal to the sum of the radius of the base and the height of the segment, divided by two.
The center of gravity of any segment of a pyramid is on its axis, at a distance from its base equal to the sum of the radius of the base and the height of the segment, divided by two.
The center of gravity of any segment of a cylinder is on its axis, at a distance from its base equal to half the height of the segment.
The center of gravity of any segment of a paraboloid of revolution is on its axis, at a distance from its base equal to two-thirds of the axis.
The center of gravity of any segment of a hyperboloid of revolution is on its axis, at a distance from its base equal to the sum of the radius of the base and the height of the segment, divided by two.
The center of gravity of any segment of an ellipsoid of revolution is on its axis, at a distance from its base equal to the sum of the radius of the base and the height of the segment, divided by two.
The center of gravity of any segment of an ellipse is on its major axis, at a distance from its center equal to the product of the eccentricity and the distance from the center to the focus.
The center of gravity of any segment of a hyperbola is on its transverse axis, at a distance from its center equal to the product of the eccentricity and the distance from the center to the focus.
The center of gravity of any segment of a parabola is on its axis, at a distance from its vertex equal to two-thirds of the distance from the vertex to the focus.
The center of gravity of any segment of a circle is on its radius, at a distance from its center equal to the product of the radius and the ratio of the chord to the arc.
The center of gravity of any segment of a spiral is on its radius vector, at a distance from its origin equal to two-thirds of the radius vector.
The center of gravity of any segment of a cone is on its axis, at a distance from its vertex equal to three-fourths of the axis.