Arts and Humanities Commons^™

From A Doodle To A Theorem: A Case Study In Mathematical Discovery, Juan FernáNdez GonzáLez, Dirk Schlimm

Journal of Humanistic Mathematics

We present some aspects of the genesis of a geometric construction, which can be carried out with compass and straightedge, from the original idea to the published version (Fernández González 2016). The Midpoint Path Construction makes it possible to multiply the length of a line segment by a rational number between 0 and 1 by constructing only midpoints and a straight line. In the form of an interview, we explore the context and narrative behind the discovery, with first-hand insights by its author. Finally, we discuss some general aspects of this case study in the context of philosophy of mathematical …

Hume's Conception Of Geometry And The Role Of Contradiction, Sofia Remedios Paz

Theses and Dissertations

David Hume’s account of geometry can seem puzzling as he claims that geometry is inexact and demonstrable. Graciela de Pierris argues for an interpretation that explains why Hume sees geometry as inexact and, yet, demonstrable. However, she doesn’t consider Hume’s description of relations of ideas found in the Enquiry. Hume distinguishes between matters of fact and relations of idea by checking to see if there is a contradiction with the denial of a proposition. Geometry is categorized as relations of idea, so the denials of geometric propositions cannot be conceivable and must imply a contradiction. I will argue that De …

Thinking Nature, "Pierre Maupertuis And The Charge Of Error Against Fermat And Leibniz", Richard Samuel Lamborn

USF Tampa Graduate Theses and Dissertations

The purpose of this dissertation is to defend Pierre Fermat and Gottfried Wilhelm Leibniz against the charge of error made against them by Pierre Maupertuis that they errantly applied final causes to physics. This charge came in Maupertuis’ 1744 speech to the Paris Academy of Sciences, later published in different versions, entitled Accord Between Different Laws Which at First Seemed Incompatible. It is in this speech that Maupertuis lays claim to one of the most important discoveries in the history of physics and science, The Principle of Least Action. From the date of this speech up until the end …

Kant On The Nature Of Geometry, James B. Gibson Jr., Dr. Michael Arts

Journal of Undergraduate Research

In the Critique of Pure Reason, Immanuel Kant develops an account of geometry which rests upon his central claim about metaphysics: that we see the world not as it may be independent of our perceiving it, but as an object of our sensible intuition. Thus, in order to understand our world, we must not only attempt to examine the world, but we must also examine the lens of our intuition, by which we perceive the world:

The Evolution And Discovery Of The Species Of Equality In Euclid’S Elements, Lee T. Nutini

Lee T Nutini

A look at the evidence for an additional and novel type of equality found in Euclid's Elements.

Chapter Vi. Proclus And Positive Negation, Raoul Mortley

Raoul Mortley

[Chapter Contents]: Desire for the One, 97; the theological Parmenides, 98; Proclus on names, 99; geometry and Euclid as the background for the via negativa, 103; privation, 106; the positive value of negation, 107; negation and privation, 108; being and negation, 109; Proclus and Hegel, 110; hypernegation, 110; negation as a test of conditional statements, 113; negation the "mother of affirmation", 114; the negation of negation and ultimate silence, 116; Beierwaltes' interpretation, 117; language rejected, 118.

The Role Of Algebraic Inferences In Naîm Ibn Mûsa’S Collection Of Geometrical Propositions, Marco Panza

MPP Published Research

Na‘im ibn Musa's lived in Baghdad in the second half of the 9th century. He was probably not a major mathematician. Still his Collection of geometrical propositions---recently edited and translated in French by Roshdi Rashed and Christian Houzel---reflects quite well the mathematical practice that was common in Thabit ibn Qurra's school. A relevant characteristic of Na‘im's treatise is its large use of a form of inferences that can be said ‘algebric' in a sense that will be explained. They occur both in proofs of theorems and in solutions of problems. In the latter case, they enter different sorts of problematic …

Studying Mathematics For The Sake Of The Good, Andrew Payne

The Society for Ancient Greek Philosophy Newsletter

In the Republic, Socrates describes the good as the end of all human action: “Every soul pursues the good and does what it does for its sake. It divines that the good is something but it is perplexed and cannot adequately grasp what it is or acquire the sort of stable beliefs it has about other things, and so it misses the benefits, if any, that even those other things may give.” I wish to examine how humans act for the sake of the good in the sections of the Republic following this passage. Human action is oriented toward the …

Redeeming The Symbols: Madeleine L'Engle And The Interpreting Of Contemporary Geometry In The Christian Tradition, C. Christopher Smith

Inklings Forever: Published Colloquium Proceedings 1997-2016

In Madeleine L’Engle’s book, A Stone for a Pillow, she discusses how the Christian faith is often concerned with redeeming symbols into something good. This paper examines the redemption of contemporary geometry and how it reflects the truths of the Christian faith.

Leonardo's Virtuvian Man: A Renaissance Microcosm, Charles Carman

Quidditas

Human nature is that nature which...elevated above all the works of God...enfolds intellectual and sensible nature...so that the ancients were right in calling it a microcosm, or a small world. Hence, human nature is that nature which, if it were elevated unto a union with Maximality, would be the fullness of all the perfections of each and every thing.

–Nicholas of Cusa