Math 1B - History of Math (Group 4)

According to Archimedes’ Principle, an object will float if:

• Its weight is greater than the buoyant force.

• Its density is less than the fluid’s density.

• The volume of displaced fluid is less than its own volume.

• The buoyant force is equal to or greater than its weight.

The famous story of Archimedes running through the streets shouting “Eureka!” was related to his discovery of:

• A method to measure volume and prove fraud

• The value of Pi

• The Law of the Lever

• The surface area of a sphere

Archimedes’ Law of the Lever states that equilibrium is achieved when:

• The products of force and distance from the fulcrum are equal.

• The forces on both sides are equal.

• The distances from the fulcrum are equal.

• The lever is perfectly horizontal.

Which of the following is NOT a real-world application of the parabola?

• The path of a thrown basketball

• The shape of a satellite dish

• The orbit of a planet around the sun

• The cable of a suspension bridge

What did Apollonius demonstrate about the parabola, ellipse, and hyperbola?

• They could only be derived from three different cone types.

• They were first discovered by Euclid.

• They were unrelated to each other geometrically.

• They could all be derived from a single, double-napped circular cone.

Which of Apollonius’s models did he use to explain the irregular motion of planets?

• Elliptical and parabolic models

• Eccentric and epicyclic models

• Hyperbolic and circular models

• Geocentric and heliocentric models

How did Archimedes approximate the value of π?

• By measuring the circumference of various circles.

• By using a physical wheel.

• By calculating the perimeters of inscribed and circumscribed 96-sided polygons

• By discovering the fraction 22/7.

Archimedes considered which of the following his greatest achievement?

• The “Method of Mechanical Theorems”

• Calculating the area of a parabolic segment

• The relationship between a sphere and its circumscribed cylinder

• Inventing the water screw

Which property defines an ellipse?

• The set of points equidistant from a focus and a directrix.

• The intersection of a plane parallel to the base of a cone.

• The set of points where the difference of distances to two foci is constant.

• The set of points where the sum of distances to two foci is constant.

Which of Archimedes’ inventions was described as a crane-like weapon used to capsize ships?

• The Improved Catapult

• The Burning Mirrors

• The Claw of Archimedes

• The Water Screw