Mechanics
Mechanics studies motion and the physical laws that describe how bodies move and interact.
The current resources focus on parabolic motion, an important example of how mathematical models describe physical trajectories and connect kinematics with algebra.
Parabolic Motion
Projectile motion combines uniform horizontal motion with uniformly accelerated vertical motion.
Its trajectory provides a direct connection between physical laws, quadratic equations, and the geometry of parabolas.
Galileo, Proof, and Parabolic Motion
My master’s thesis examines the relationship between mathematics and physics education through the historical case of Galileo’s demonstration of parabolic motion.
It compares Galileo’s geometric argument with a modern algebraic derivation, considering how different forms of proof describe the same physical phenomenon and perform different explanatory and educational functions. The thesis also presents a teaching module developed within the European IDENTITIES project and an analysis of its implementation with prospective mathematics and physics teachers.
Was Tartaglia Galileo’s Teacher?
Niccolò Tartaglia was not Galileo’s teacher: Tartaglia died in 1557, seven years before Galileo was born. The connection is indirect. Galileo attended a course on Euclid taught by Ostilio Ricci, a former pupil of Tartaglia, and studied Euclid and Archimedes through Tartaglia’s Italian translations.
The thesis discusses Tartaglia’s earlier representation of projectile motion as part of the historical background to Galileo’s demonstration of the parabolic trajectory.
For the biographical chronology and the connection through Ricci, see the MacTutor biographies of Tartaglia and Galileo.
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Mathematics and Motion
Parabolic motion is a particularly clear example of the relationship between mathematics and physics.
A quadratic equation is not only an abstract algebraic object: under appropriate physical assumptions, the same mathematical structure describes the trajectory of a projectile.
This connection illustrates one of the central ideas of mathematical physics — different ways of describing a phenomenon can reveal the same underlying structure.