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2018, The Ormsby Review
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In "Euclid's Orchard and Other Essays," Theresa Kishkan reflects on the interplay between the personal, the mathematical, and the natural world through a meditative exploration of her experiences in an orchard. The work intricately weaves memories and sensory details, particularly of apples and their transformation into apple butter, with the concept of Euclid's orchard—a thought experiment that explores visibility and obscurity through the lens of geometry. Through vivid imagery and contemplative prose, Kishkan articulates a deeper understanding of connection to place, family, and the nuances of life, emphasizing the beauty found in both intricate patterns and the everyday moments that define existence.
Journal of Mathematics and the Arts
2015
In 2007—possibly earlier—I started to write a paper entitled Euclid’s straight lines. During the academic year 2010-2011 I studied Classical Greek for Ove Strid in order to improve my understanding of Euclid (but not only). I was aware that publication might be a problem, since the paper contained too much of Classical Greek for a mathematics journal, and too much mathematics for a language journal. I submitted it three times without success. The fourth time the paper was accepted. This note tells the story of my attempts . . . maybe somebody could learn something from my experience . . . perhaps even beyond the ever-present
2019
We show how a network of ideas —a forest of trees—that constitute a 3-D tree graph of a proof in geometry both interact and accumulate in number and kind. Our bar graphs, adjacency matrices, and a new 3-D glass and wood sculpture represent ways to visualize a geometry proof (in our case, the Pythagorean Theorem) and its interacting premises. Perspective from the Tree Proving Euclid’s propositions from his Elements is one thing. Graphing them, on the other hand, seems a “no-go.” Recently, in MathOverflow, a Q. & A. math website, this query appeared: “Is anyone aware of any attempt to describe the dependencies of theorems [propositions]...in the form of a family tree [tree graph]... where each node on the tree might correspond to a theorem and branches would indicate dependencies between theorems” [9]? The answer is: Yes! That is what we do. Our colleague, Jesse Atkinson, is the first, publishing in the Bridges Math/Art Conference Proceedings (2016) [1] and exhibiting in the Conferenc...
Applied Mathematics and Computation, 2004
Part of the attraction of Euclid geometry is that almost all of its theorems can be pictorially confirmed. In this study; focusing on the concept of area in the plane geometry it has been showed that the areas have been invariant with various arrangements made without the data of a geometric figure making use of area axioms.
Synthese, 2012
The Mathematical Intelligencer
Filomat, 2009
Sketching and computer visualization are standard communication media in Technology and Natural Science as well as in Mathematics. Of any visualization we demand easy interpretability by the 'educated' viewer not only can 'read' the meaning of the figure but also gains some understanding of the visualized problem. Such a 'visual communication' needs schooling and training. Descriptive Geometry provides some simple but effective rules and techniques for such a visual communication. Using properties classical geometric mappings, e.g. normal projections or cyclography, can give insight to problems, which sometimes are rather hard to tackle purely by mathematical calculation. Sometimes we receive even an easy proof of the problem, a proof 'by looking at the figure', such that one is encouraged to speak of a 'geometric royal road' to the problem. Some special examples of such problems shall illustrate this statement. Most of the shown examples are ...
Normat, 2015
This is the accepted version of a paper published in Normat. This paper has been peer-reviewed but does not include the final publisher proof-corrections or journal pagination.
Nexus network journal/Nexus Network Journal, 2024
Can we compute what we cannot draw? How must we draw to produce measurable representations, or visual ones? This research inquires into the relationship between mathematics and figurative representation, and more precisely between drawing and computation. The scientific imagery studied here is the representation of the five platonic solids, discussing various representation techniques from classical antiquity to modern times, and their efficacy to help calculate sizes and proportional ratios. Scholars in history of architectural drawing have too often limited their observations to the very few preserved plans and front views dating back to classical antiquity, without enlarging their investigation to other scientific fields that also rely on drawing as a research tool and communication device. Among these other fields stands the mathematical research, especially solid geometry which deals with objects and entities that have shapes that needs to be somehow drawn in 3D to be studied.
2004
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