Archimedes

The method of mechanical theorems is a way to discover mathematical truths by considering them as problems in mechanics.

The center of gravity of a segment of a parabola is on the diameter of the segment, and its distance from the vertex is 3/5 of the length of the diameter.

The area of an ellipse is pi times the product of its semi-major and semi-minor axes.

The law of the lever states that when a lever is in equilibrium, the product of the force and its distance from the fulcrum on one side is equal to the product of the force and its distance from the fulcrum on the other side.

The number of grains of sand that could be contained in the universe is less than 10^63.

The properties of the sphere and cylinder are among the most beautiful and important in geometry.

The method of exhaustion is a rigorous way to prove the results obtained by the method of mechanical theorems.

The area of a segment of a circle is equal to the area of a sector with the same radius and central angle, minus the area of the triangle formed by the radii and the chord.

The center of gravity of a hemisphere is on its axis, and its distance from the base is 3/8 of the radius.

The volume of a segment of a sphere is equal to the volume of a cone with the same base and height, plus the volume of a cylinder with the same base and height, minus the volume of a cone with the same base and height.

The properties of the spiral are useful for squaring the circle and trisecting an angle.

The method of exhaustion is a powerful tool for calculating areas and volumes of complex shapes.

The center of gravity of a parabola is on its axis, and its distance from the vertex is 3/5 of the length of the axis.

The volume of a segment of a paraboloid is half the volume of the cylinder with the same base and height.

The properties of the sphere and cylinder are a testament to the beauty and order of the universe.

The method of mechanical theorems allows us to discover mathematical truths by analogy with physical principles.

The area of a segment of an ellipse is equal to the area of a sector with the same radii and central angle, minus the area of the triangle formed by the radii and the chord.

The center of gravity of a segment of a sphere is on its axis, and its distance from the base is 3/8 of the height of the segment.

The volume of a segment of a hyperboloid is equal to the volume of a cone with the same base and height, plus the volume of a cylinder with the same base and height, minus the volume of a cone with the same base and height.

The properties of the spiral are a rich source of mathematical problems and insights.