Open Access. Powered by Scholars. Published by Universities.®
Physical Sciences and Mathematics Commons™
Open Access. Powered by Scholars. Published by Universities.®
- Keyword
-
- Geometry (2)
- Centroid (1)
- Circle packing (1)
- Combinatorics (1)
- Contemplation (1)
-
- Contemplative education (1)
- Coordinate proof (1)
- Curves (1)
- Escher (1)
- Fichtner (1)
- Figurate number (1)
- Fresco (1)
- Graph theory (1)
- Hexagram (1)
- Intersubjectivity (1)
- Lee-Hamilton (1)
- Logarithmic spiral (1)
- Love (1)
- Math (1)
- Mathematics (1)
- Mathematics in art (1)
- Mazzola (1)
- Meditation (1)
- Pappus of Alexandria (1)
- Pattern blocks (1)
- Pattern blocks; congruence; geometry (1)
- Paulus of Middelburg (1)
- Poem (1)
- Polygonal number (1)
- Proof without words (1)
Articles 1 - 11 of 11
Full-Text Articles in Physical Sciences and Mathematics
One Theorem, Two Ways: A Case Study In Geometric Techniques, John B. Little
One Theorem, Two Ways: A Case Study In Geometric Techniques, John B. Little
Journal of Humanistic Mathematics
If the three sides of a triangle ABΓ in the Euclidean plane are cut by points H on AB, Θ on BΓ, and K on ΓA cutting those sides in same ratios:
AH : HB = BΘ : ΘΓ = ΓK : KA,
then Pappus of Alexandria proved that the triangles ABΓ and HΘK have the same centroid (center of mass). We present two proofs of this result: an English translation of Pappus's original synthetic proof and a modern algebraic proof making use of Cartesian coordinates and vector concepts. Comparing the two methods, we can see that while the algebraic …
Plane Figurate Number Proofs Without Words Explained With Pattern Blocks, Gunhan Caglayan
Plane Figurate Number Proofs Without Words Explained With Pattern Blocks, Gunhan Caglayan
Journal of Humanistic Mathematics
This article focuses on an artistic interpretation of pattern block designs with primary focus on the connection between pattern blocks and plane figurate numbers. Through this interpretation, it tells the story behind a handful of proofs without words (PWWs) that are inspired by such pattern block designs.
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.
Pattern Blocks Art, Gunhan Caglayan
Pattern Blocks Art, Gunhan Caglayan
Journal of Humanistic Mathematics
Pattern blocks are versatile manipulatives facilitating connections that can be made among various strands of mathematics such as number sense, algebra, geometry and measurement, spatial reasoning, probability and trigonometry. This note focuses on an artistic interpretation of the pattern blocks with primary focus on convex polygons made with pattern blocks, and describes five mathematically rich activities using them.
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 …
Geometry Of Life, Janice Dykacz
Geometry Of Life, Janice Dykacz
Journal of Humanistic Mathematics
Relationships in life can be expressed through geometric curves
My Finite Field, Matthew Schroeder
My Finite Field, Matthew Schroeder
Journal of Humanistic Mathematics
A love poem written in the language of mathematics.
Abscissas And Ordinates, David Pierce
Abscissas And Ordinates, David Pierce
Journal of Humanistic Mathematics
In the manner of Apollonius of Perga, but hardly any modern book, we investigate conic sections as such. We thus discover why Apollonius calls a conic section a parabola, an hyperbola, or an ellipse; and we discover the meanings of the terms abscissa and ordinate. In an education that is liberating and not simply indoctrinating, the student of mathematics will learn these things.
On Contemplation In Mathematics, Frank Lucas Wolcott
On Contemplation In Mathematics, Frank Lucas Wolcott
Journal of Humanistic Mathematics
In a section about research, we make the case that intentional, structured reflection on the mathematical research process, by mathematical researchers themselves, would result in better mathematicians doing better mathematics. As supporting evidence, we describe the Flavors and Seasons project. In a section about teaching, we describe the contemplative education movement and share personal experiences using meditation in the math classroom. We conclude with an explicit proposal for elucidating the experiential context of mathematics, in both research and teaching environments.
Raphael's School Of Athens: A Theorem In A Painting?, Robert Haas
Raphael's School Of Athens: A Theorem In A Painting?, Robert Haas
Journal of Humanistic Mathematics
Raphael's famous painting The School of Athens includes a geometer, presumably Euclid himself, demonstrating a construction to his fascinated students. But what theorem are they all studying? This article first introduces the painting, and describes Raphael's lifelong friendship with the eminent mathematician Paulus of Middelburg. It then presents several conjectured explanations, notably a theorem about a hexagram (Fichtner), or alternatively that the construction may be architecturally symbolic (Valtieri). The author finally offers his own "null hypothesis": that the scene does not show any actual mathematics, but simply the fascination, excitement, and joy of mathematicians at their work.
Logarithmic Spirals And Projective Geometry In M.C. Escher's "Path Of Life Iii", Heidi Burgiel, Matthew Salomone
Logarithmic Spirals And Projective Geometry In M.C. Escher's "Path Of Life Iii", Heidi Burgiel, Matthew Salomone
Journal of Humanistic Mathematics
M.C. Escher's use of dilation symmetry in Path of Life III gives rise to a pattern of logarithmic spirals and an oddly ambiguous sense of depth.