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

By Jacques Fleuriot PhD, MEng (auth.)

Sir Isaac Newton's philosophi Naturalis Principia Mathematica'(the Principia) features a prose-style mix of geometric and restrict reasoning that has frequently been considered as logically vague.
In A blend of Geometry Theorem Proving and NonstandardAnalysis, Jacques Fleuriot provides a formalization of Lemmas and Propositions from the Principia utilizing a mix of equipment from geometry and nonstandard research. The mechanization of the methods, which respects a lot of Newton's unique reasoning, is built in the theorem prover Isabelle. the appliance of this framework to the mechanization of uncomplicated actual research utilizing nonstandard recommendations is additionally discussed.

Show description

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

Similar geometry books

Asymptotics in dynamics, geometry and PDEs; Generalized Borel Summation. / vol. II

This booklet is dedicated to the mathematical and numerical research of the inverse scattering challenge for acoustic and electromagnetic waves. the second one variation comprises fabric on Newton’s technique for the inverse problem challenge, a chic evidence of area of expertise for the inverse medium challenge, a dialogue of the spectral thought of the a ways box operator and a style for picking the aid of an inhomogeneous medium from some distance box info Feynman graphs in perturbative quantum box thought / Christian Bogner and Stefan Weinzierl -- The flexion constitution and dimorphy: flexion devices, singulators, turbines, and the enumeration of multizeta irreducibles / Jean Ecalle -- at the parametric resurgence for a definite singularly perturbed linear differential equation of moment order / Augustin Fruchard and Reinhard Schäfke -- On a Schrödinger equation with a merging pair of an easy pole and a straightforward turning aspect - Alien calculus of WKB strategies via microlocal research / Shingo Kamimoto, Takahiro Kawai, Tatsuya Koike and Yoshitsugu Takei -- at the turning element challenge for instanton-type suggestions of Painlevé equations / Yoshitsugu Takei

Basic noncommutative geometry

"Basic Noncommutative Geometry presents an creation to noncommutative geometry and a few of its purposes. The e-book can be utilized both as a textbook for a graduate path at the topic or for self-study. it will likely be priceless for graduate scholars and researchers in arithmetic and theoretical physics and all people who find themselves drawn to gaining an figuring out of the topic.

3-D Shapes Are Like Green Grapes!

- huge variety, considerable spacing among phrases and features of textual content- Easy-to-follow structure, textual content seems at comparable position on pages in each one part- universal gadgets and issues- Use of excessive frequency phrases and extra complicated vocabulary- colourful, enticing photographs and imagine phrases offer excessive to reasonable aid of textual content to aid with note attractiveness and mirror multicultural range- various punctuation- helps nationwide arithmetic criteria and learner results- Designed for school room and at-home use for guided, shared, and self sufficient interpreting- Full-color images- Comprehension task- thesaurus

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

Sample text

X n + Y n})" hypreal_Iess_def "p < (Q:: hypreal) == 3x Y. XERep_hypreal (p) A YERep_hypreal(Q) A {n: :nat. 3. 1 Choosing a Free Ultrafilter To start the construction, a free ultrafilter UIN is chosen on the set of natural numbers IN. There exists one according to the Weak Ultrafilter Theorem: (WUF) Weak Ultrafilter Theorem. There exists a free ultrafilter on IN. As can be seen, this is a special case of the UFT corollary from the last section. In fact, we have the implications AC => UFT => WUF, which are not reversible.

This result can be proved using Zorn's Lemma. In fact, we are really interested in proving a corollary of UFT about the existence of free ultrafilters: 1 1 Some authors like Hoskins (48) and Keisler [52) state the corollary (or even one of its special cases) as the actual Ultrafilter Theorem. 44 3. Constructing the Hyperreals Corollary. On every infinite set there exists a free ultrafilter. ,finite S ==> 3u. u E FreeUltrafilters S To do so, we define in the theory Filter the set, SuperFrechet S, of all filters on S that contain the Fnkhet filter (Le.

The usual approach is to arrange them in a lattice respecting the inclusions between the sets. Let 2Z,

Download PDF sample

Rated 4.37 of 5 – based on 42 votes