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Articles 1 - 15 of 15
Full-Text Articles in Physical Sciences and Mathematics
Could Raphael’S School Of Athens Contain Hidden Geometry?, Frode S. Larsen, Harald E. Moe
Could Raphael’S School Of Athens Contain Hidden Geometry?, Frode S. Larsen, Harald E. Moe
Journal of Humanistic Mathematics
In this article we argue that Raphael has hidden a geometric shape called a vesica piscis in his fresco The School of Athens (1510-1511). The vesica piscis, and several findings which can be interpreted as suggesting the presence of a vesica piscis in the fresco, are presented. Several of these suggestions relate to the vesica piscis drawn in the construction of an equilateral triangle in the first proposition of Euclid’s Elements. Based on findings in the fresco, we suggest that the vesica piscis should be interpreted in light of a philosophical and theological controversy which took place in Italy …
From A Doodle To A Theorem: A Case Study In Mathematical Discovery, Juan FernáNdez GonzáLez, Dirk Schlimm
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 …
Crocheting Mathematics Through Covid-19, Beyza C. Aslan
Crocheting Mathematics Through Covid-19, Beyza C. Aslan
Journal of Humanistic Mathematics
As it is often said, something good often comes out of most bad situations. The time I spent during COVID-19, at home and isolated with my two children, brought out one secret passion in me: crocheting. Not only did it help me pass the time in a sane and productive way, but also it gave me a new goal in life. It connected my math side with my artistic side. It gave me a new perspective to look at math, and helped me help others see math in a positive way.
Making Art In Math Class During The Pandemic, Larson Fairbairn, Kameelah Jackson, Ksenija Simic-Muller
Making Art In Math Class During The Pandemic, Larson Fairbairn, Kameelah Jackson, Ksenija Simic-Muller
Journal of Humanistic Mathematics
For many of us, the pandemic has changed how we teach and how we support students. This manuscript highlights creativity as a way to support for student mathematical and emotional well-being. It describes the positive impact that creative assignments in a mathematics content course for preservice K-8 teachers had on students during the early days of the pandemic. The story is told by the instructor and two former students in the course.
One Straight Line Addresses Another Traveling In The Same Direction On An Infinite Plane, Daniel W. Galef
One Straight Line Addresses Another Traveling In The Same Direction On An Infinite Plane, Daniel W. Galef
Journal of Humanistic Mathematics
No abstract provided.
Geometry Of Night, Jenny Patton
Geometry Of Night, Jenny Patton
Journal of Humanistic Mathematics
No abstract provided.
Descartes Comes Out Of The Closet, Nora E. Culik
Descartes Comes Out Of The Closet, Nora E. Culik
Journal of Humanistic Mathematics
While “Descartes Comes Out of the Closet” is ostensibly about a young woman’s journey to Paris, the descriptive detail borrows language and images from Cartesian coordinate geometry, dualistic philosophy, neuroanatomy (the pineal), and projections of three dimensions onto planes. This mathematical universe is counterpointed in the natural language of the suppressed love story that locates the real in the human. Thus, at the heart of the story is the tension between competing notions of mathematics, i.e., as either an independent realm apart from history or as a culturally produced and historical set of practices. Of course, the central character proves …
Paul's Dilemma: Is This A Polyhedron?, Bethany Noblitt, Shelly Harkness
Paul's Dilemma: Is This A Polyhedron?, Bethany Noblitt, Shelly Harkness
Journal of Humanistic Mathematics
Teachers play the believing game when they honor students’ mathematical thinking, even when it means they must suspend their own mathematical thinking momentarily. The study reported here tells the story of what happened in a university mathematics classroom when one student did not think that a particular figure satisfied the definition of a polyhedron and the instructor chose to play the believing game. The result was a very rich discussion, where both students and the authors grappled with their own mathematical understanding. One author served as the instructor of the course and the other author was an observer, taking field …
Patterns Formed By Coins, Andrey M. Mishchenko
Patterns Formed By Coins, Andrey M. Mishchenko
Journal of Humanistic Mathematics
This article is a gentle introduction to the mathematical area known as circle packing, the study of the kinds of patterns that can be formed by configurations of non- overlapping circles. The first half of the article is an exposition of the two most important facts about circle packings, (1) that essentially whatever pattern we ask for, we may always arrange circles in that pattern, and (2) that under simple conditions on the pattern, there is an essentially unique arrangement of circles in that pattern. In the second half of the article, we consider related questions, but where we …
Propeller, Joel Kahn
Propeller, Joel Kahn
The STEAM Journal
This image is based on several different algorithms interconnected within a single program in the language BASIC-256. The fundamental structure involves a tightly wound spiral working outwards from the center of the image. As the spiral is drawn, different values of red, green and blue are modified through separate but related processes, producing the changing appearance. Algebra, trigonometry, geometry, and analytic geometry are all utilized in overlapping ways within the program. As with many works of algorithmic art, small changes in the program can produce dramatic alterations of the visual output, which makes lots of variations possible.
A Space-Filling, Nonregular Tetrahedron, Margaret Cagle, Joyce Frost, Christine Latulippe, Darryl H. Yong
A Space-Filling, Nonregular Tetrahedron, Margaret Cagle, Joyce Frost, Christine Latulippe, Darryl H. Yong
All HMC Faculty Publications and Research
This activity is an investigation of a special nonregular tetrahedron that can be arranged to fill space without leaving any internal gaps in the same way that certain planar figures tessellate the plane. These tetrahedra can be connected together with hinges to make fun and interesting puzzles. More background information can be found in the paper "An Amazing, Space-Filling, Non-Regular Tetrahedron" by Joyce Frost and Peg Cagle, published by the IAS/Park City Mathematics Institute (available at mathforum.org/pcmi/hstp/resources/dodeca/).
The Mathematical Landscape, Antonio Collazo
The Mathematical Landscape, Antonio Collazo
CMC Senior Theses
The intent of this paper is to present the reader will enough information to spark a curiosity in to the subject. By no means is the following a complete formulation of any of the topics covered. I want to give the reader a tour of the mathematical landscape. There are plenty of further details to explore in each section, I have just touched the tip the iceberg. The work is basically in four sections: Numbers, Geometry, Functions, Sets and Logic, which are the basic building blocks of Math. The first sections are a exposition into the mathematical objects and their …
Noisy Signal Recovery Via Iterative Reweighted L1-Minimization, Deanna Needell
Noisy Signal Recovery Via Iterative Reweighted L1-Minimization, Deanna Needell
CMC Faculty Publications and Research
Compressed sensing has shown that it is possible to reconstruct sparse high dimensional signals from few linear measurements. In many cases, the solution can be obtained by solving an L1-minimization problem, and this method is accurate even in the presence of noise. Recent a modified version of this method, reweighted L1-minimization, has been suggested. Although no provable results have yet been attained, empirical studies have suggested the reweighted version outperforms the standard method. Here we analyze the reweighted L1-minimization method in the noisy case, and provide provable results showing an improvement in the error bound over the standard bounds.
A Theoretical Investigation Of The Geometries, Vibrational Frequencies, And Binding Energies Of Several Mixed Alkali Halide Dimers, Robert J. Cave, Ian Ono '94
A Theoretical Investigation Of The Geometries, Vibrational Frequencies, And Binding Energies Of Several Mixed Alkali Halide Dimers, Robert J. Cave, Ian Ono '94
All HMC Faculty Publications and Research
Results are presented from ab initio calculations on several mixed alkali halide dimers made up of Li, Na, F, and Cl. All of the dimers are investigated at the restricted Hartree–Fock level to provide ab initio estimates of geometries, vibrational frequencies, and binding energies. The dimer LiNaF2 is then treated using a variety of basis sets at the Hartree–Fock level, as well as at correlated levels (second‐order Møller–Plesset and coupled‐cluster singles and doubles) to examine the sensitivity of the calculations to use of higher levels of theory. The results are then compared to the experimental data available for the LiNaF2 …
A Theoretical Investigation Of The Geometries, Vibrational Frequencies, And Binding Energies Of Several Alkali Halide Dimers, Robert P. Dickey '93, David Maurice '91, Robert J. Cave, Richard J. Mawhorter
A Theoretical Investigation Of The Geometries, Vibrational Frequencies, And Binding Energies Of Several Alkali Halide Dimers, Robert P. Dickey '93, David Maurice '91, Robert J. Cave, Richard J. Mawhorter
All HMC Faculty Publications and Research
Results are presented from ab initio calculations on the symmetrical alkali halide dimers made up of Li, Na, K, F, and Cl. We examine the sensitivity of representative monomer and dimer geometries to the variation of the basis set with and without polarization and diffuse functions. The geometries are then compared with available experimental results. We have also calculated vibrational frequencies at the restricted Hartree–Fock level and examined the changes in geometry brought about by correlation using second‐order Møller–Plesset perturbation theory. It is found that Hartree–Fock theory in a modest basis set with diffuse and polarization functions yields results comparable …