Download A Combination of Geometry Theorem Proving and Nonstandard by Jacques Fleuriot PhD, MEng (auth.) PDF

By Jacques Fleuriot PhD, MEng (auth.)

ISBN-10: 1447110412

ISBN-13: 9781447110415

Sir Isaac Newton's philosophi Naturalis Principia Mathematica'(the Principia) encompasses a prose-style mix of geometric and restrict reasoning that has frequently been seen as logically vague.
In A mix of Geometry Theorem Proving and NonstandardAnalysis, Jacques Fleuriot provides a formalization of Lemmas and Propositions from the Principia utilizing a mixture of equipment from geometry and nonstandard research. The mechanization of the methods, which respects a lot of Newton's unique reasoning, is constructed in the theorem prover Isabelle. the applying of this framework to the mechanization of hassle-free genuine research utilizing nonstandard recommendations is usually discussed.

Show description

Read Online or Download A Combination of Geometry Theorem Proving and Nonstandard Analysis with Application to Newton’s Principia PDF

Similar geometry books

Fractals Everywhere: The First Course in Deterministic Fractal Geometry

This version additionally good points extra difficulties and instruments emphasizing fractal functions, in addition to a brand new solution key to the textual content routines.

Dynamical Systems X: General Theory of Vortices

The English train mechanics as an experimental technological know-how, whereas at the Continent, it has consistently been thought of a extra deductive and a priori technological know-how. absolutely, the English are correct. * H. Poincare, technology and speculation Descartes, Leibnitz, and Newton As is widely known, the fundamental ideas of dynamics have been said by means of New­ ton in his recognized paintings Philosophiae Naturalis Principia Mathematica, whose e-book in 1687 was once paid for by means of his good friend, the astronomer Halley.

The Geometry of Jet Bundles

The aim of this booklet is to supply an creation to the idea of jet bundles for mathematicians and physicists who desire to examine differential equations, rather these linked to the calculus of adaptations, in a contemporary geometric method. one of many topics of the booklet is that first-order jets might be regarded as the average generalisation of vector fields for learning variational difficulties in box conception, and such a lot of of the buildings are brought within the context of first- or second-order jets, sooner than being defined of their complete generality.

Additional resources for A Combination of Geometry Theorem Proving and Nonstandard Analysis with Application to Newton’s Principia

Example text

It is often easy to omit non-degenerate conditions especially when the user formulates a theorem to be proved using a diagram as a guide. We tend to draw on paper "well-formed" diagrams that enable us to picture the property we are trying to prove. However, for the automatic theorem prover, if the necessary conditions are not available then it might fail to find a proof. For example, in 24 2. Geometry Theorem Proving a parallelogram ABCD, the two diagonals AC and BD bisect each other if A, B, C and D are not collinear.

PRAT = PMAT + Equiv + constdefs (* equivalence relation *) pratrel :: "«pnat * pnat) * (pnat * pnat» set" "pratrel {p. 3 abc d. p = «a,b), (c,d» " ad = bc}" = typedef prat = "{x:: (pnat*pnat). quotient_def) instance prat :: {ord, plUS, times} constdefs prat_oCpnat :: pnat ::} prat (11$#_" [80] 80) "prat_oCpnat m Abs_prat(pratrel-A{(m,Abs_pnat i)})" = qinv :: prat ::} prat "qinv Q Abs_prat(U(x,y)ERep_prat(Q). pratrel AA{(y ,x)}) II = defs prat_add_def IIp + Q Abs_prat (UpERep_prat (P). ~a b. ~c d.

1. 2 and on the definition of parallel lines. The following goal with its associated premises now results: [Is_delta CAP = s_delta Q B P + s_delta B A Pj s_delta R P A = s_delta B Q A + s_delta Q PAl] ==> s_delta CAP = -s_delta R P A The next steps are trivial and follow from the theorems we proved about areas of quadrilaterals. The subgoals are routinely proved by Isabelle's simplifier, thereby proving Pascal's theorem. We give a rather more detailed Isabelle proof to show the area method at work.

Download PDF sample

Rated 5.00 of 5 – based on 10 votes