Jay Kappraff
Encyclopedia
Jay Kappraff is a American
professor
of mathematics
at the New Jersey Institute of Technology
and author
.
, physical sciences and mathematics
, earning a B.Ch.E. in Chemical Engineering
at New York Polytechnic in 1958. He went on to be awarded a Ph.D.
in Applied Mathematics in 1974 from the Courant Institute of Mathematical Science, New York University
and a M.S. in Chemical Engineering in 1960 from Iowa State University
. He began work for Dupont
DeNemours as a Chemical Engineer from 1961 to 1962 going on to teach mathematics for a brief period before obtaining a position at NASA
as an aerospace engineer from 1962 until 1965. He went on to be an instructor of mathematics at the Cooper Union College, New York
from 1968 until 1974. Following this, he joined the New Jersey Institute of Technology where he currently works. He was a consultant for the Department of Energy
in 1976. In 1978 he developed a course in the mathematics of design for computer scientist
s, mathematician
s and architect
s. In bringing together such an interdisciplinary range of subjects, he began to study what he termed a common language of design and geometry
. He has been a prolific lecturer on the relationship between art
and science
and published a large number or articles on subjects ranging from plasma physics, solar heating, aerospace engineering
and fractals. He has also published a number of books on these and related subjects and compiled a series of video lectures on the science of design. He is a skilled musician and a member of a Baroque
ensemble, President of a local civic
group and has organized a Chamber Music Workshop writing and directing a program entitled The Musicians and Artists of Terezin
. He has also assisted a task force to improve voting machines in New Jersey
. His other interests include playing violin
and tennis
, listening to chamber music
and practicing t'ai chi.
In 1991 his book Connections won a prize for the best book in chemistry
, physics
, mathematics
, astronomy
and reference from the Association of American Publishers
.
to experimental mathematics
. he is a member of the faculty council and chairman of the NJIT Technology
and Society
Forum committee. He is a member of the Mathematics Association of America and on the editorial board of a new interdisciplinary journal, the International Journal of Biological Systems. He was also guest editor of the journal FORMA for a special issue on the Golden Mean
in 2005.
United States
The United States of America is a federal constitutional republic comprising fifty states and a federal district...
professor
Professor
A professor is a scholarly teacher; the precise meaning of the term varies by country. Literally, professor derives from Latin as a "person who professes" being usually an expert in arts or sciences; a teacher of high rank...
of mathematics
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
at the New Jersey Institute of Technology
New Jersey Institute of Technology
New Jersey Institute of Technology is a public research university in Newark, New Jersey. It is often also referred to as Newark College of Engineering ....
and author
Author
An author is broadly defined as "the person who originates or gives existence to anything" and that authorship determines responsibility for what is created. Narrowly defined, an author is the originator of any written work.-Legal significance:...
.
Biography
Kappraff was trained in engineeringEngineering
Engineering is the discipline, art, skill and profession of acquiring and applying scientific, mathematical, economic, social, and practical knowledge, in order to design and build structures, machines, devices, systems, materials and processes that safely realize improvements to the lives of...
, physical sciences and mathematics
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
, earning a B.Ch.E. in Chemical Engineering
Chemical engineering
Chemical engineering is the branch of engineering that deals with physical science , and life sciences with mathematics and economics, to the process of converting raw materials or chemicals into more useful or valuable forms...
at New York Polytechnic in 1958. He went on to be awarded a Ph.D.
Ph.D.
A Ph.D. is a Doctor of Philosophy, an academic degree.Ph.D. may also refer to:* Ph.D. , a 1980s British group*Piled Higher and Deeper, a web comic strip*PhD: Phantasy Degree, a Korean comic series* PhD Docbook renderer, an XML renderer...
in Applied Mathematics in 1974 from the Courant Institute of Mathematical Science, New York University
New York University
New York University is a private, nonsectarian research university based in New York City. NYU's main campus is situated in the Greenwich Village section of Manhattan...
and a M.S. in Chemical Engineering in 1960 from Iowa State University
Iowa State University
Iowa State University of Science and Technology, more commonly known as Iowa State University , is a public land-grant and space-grant research university located in Ames, Iowa, United States. Iowa State has produced astronauts, scientists, and Nobel and Pulitzer Prize winners, along with a host of...
. He began work for Dupont
Dupont
-Companies:*E.I. du Pont de Nemours and Company , one of the world's largest chemical companies*Du Pont Motors*Gilbert Dupont, a French stock brokerage part of retail banking network Crédit du Nord...
DeNemours as a Chemical Engineer from 1961 to 1962 going on to teach mathematics for a brief period before obtaining a position at NASA
NASA
The National Aeronautics and Space Administration is the agency of the United States government that is responsible for the nation's civilian space program and for aeronautics and aerospace research...
as an aerospace engineer from 1962 until 1965. He went on to be an instructor of mathematics at the Cooper Union College, New York
New York
New York is a state in the Northeastern region of the United States. It is the nation's third most populous state. New York is bordered by New Jersey and Pennsylvania to the south, and by Connecticut, Massachusetts and Vermont to the east...
from 1968 until 1974. Following this, he joined the New Jersey Institute of Technology where he currently works. He was a consultant for the Department of Energy
United States Department of Energy
The United States Department of Energy is a Cabinet-level department of the United States government concerned with the United States' policies regarding energy and safety in handling nuclear material...
in 1976. In 1978 he developed a course in the mathematics of design for computer scientist
Computer scientist
A computer scientist is a scientist who has acquired knowledge of computer science, the study of the theoretical foundations of information and computation and their application in computer systems....
s, mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
s and architect
Architect
An architect is a person trained in the planning, design and oversight of the construction of buildings. To practice architecture means to offer or render services in connection with the design and construction of a building, or group of buildings and the space within the site surrounding the...
s. In bringing together such an interdisciplinary range of subjects, he began to study what he termed a common language of design and geometry
Geometry
Geometry arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers ....
. He has been a prolific lecturer on the relationship between art
Art
Art is the product or process of deliberately arranging items in a way that influences and affects one or more of the senses, emotions, and intellect....
and science
Science
Science is a systematic enterprise that builds and organizes knowledge in the form of testable explanations and predictions about the universe...
and published a large number or articles on subjects ranging from plasma physics, solar heating, aerospace engineering
Aerospace engineering
Aerospace engineering is the primary branch of engineering concerned with the design, construction and science of aircraft and spacecraft. It is divided into two major and overlapping branches: aeronautical engineering and astronautical engineering...
and fractals. He has also published a number of books on these and related subjects and compiled a series of video lectures on the science of design. He is a skilled musician and a member of a Baroque
Baroque
The Baroque is a period and the style that used exaggerated motion and clear, easily interpreted detail to produce drama, tension, exuberance, and grandeur in sculpture, painting, literature, dance, and music...
ensemble, President of a local civic
Civic
Civic can refer to multiple things:*Civics, the science of comparative government*Civic, Christchurch, a Category II heritage building in the Christchurch Central City*Civic engagement, the connection one feels with their larger community...
group and has organized a Chamber Music Workshop writing and directing a program entitled The Musicians and Artists of Terezin
Terezín
Terezín is the name of a former military fortress and adjacent walled garrison town in the Ústí nad Labem Region of the Czech Republic.-Early history:...
. He has also assisted a task force to improve voting machines in New Jersey
New Jersey
New Jersey is a state in the Northeastern and Middle Atlantic regions of the United States. , its population was 8,791,894. It is bordered on the north and east by the state of New York, on the southeast and south by the Atlantic Ocean, on the west by Pennsylvania and on the southwest by Delaware...
. His other interests include playing violin
Violin
The violin is a string instrument, usually with four strings tuned in perfect fifths. It is the smallest, highest-pitched member of the violin family of string instruments, which includes the viola and cello....
and tennis
Tennis
Tennis is a sport usually played between two players or between two teams of two players each . Each player uses a racket that is strung to strike a hollow rubber ball covered with felt over a net into the opponent's court. Tennis is an Olympic sport and is played at all levels of society at all...
, listening to chamber music
Chamber music
Chamber music is a form of classical music, written for a small group of instruments which traditionally could be accommodated in a palace chamber. Most broadly, it includes any art music that is performed by a small number of performers with one performer to a part...
and practicing t'ai chi.
In 1991 his book Connections won a prize for the best book in chemistry
Chemistry
Chemistry is the science of matter, especially its chemical reactions, but also its composition, structure and properties. Chemistry is concerned with atoms and their interactions with other atoms, and particularly with the properties of chemical bonds....
, physics
Physics
Physics is a natural science that involves the study of matter and its motion through spacetime, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.Physics is one of the oldest academic...
, mathematics
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
, astronomy
Astronomy
Astronomy is a natural science that deals with the study of celestial objects and phenomena that originate outside the atmosphere of Earth...
and reference from the Association of American Publishers
Association of American Publishers
The Association of American Publishers is the national trade association of the American book publishing industry. AAP has more than 300 members, including most of the major commercial publishers in the United States, as well as smaller and non-profit publishers, university presses and scholarly...
.
Professional activities
At the NJIT, Kapraff has organized various forums and tuition programs on subjects from Nuclear war and ancient geometryGeometry
Geometry arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers ....
to experimental mathematics
Experimental mathematics
Experimental mathematics is an approach to mathematics in which numerical computation is used to investigate mathematical objects and identify properties and patterns...
. he is a member of the faculty council and chairman of the NJIT Technology
Technology
Technology is the making, usage, and knowledge of tools, machines, techniques, crafts, systems or methods of organization in order to solve a problem or perform a specific function. It can also refer to the collection of such tools, machinery, and procedures. The word technology comes ;...
and Society
Society
A society, or a human society, is a group of people related to each other through persistent relations, or a large social grouping sharing the same geographical or virtual territory, subject to the same political authority and dominant cultural expectations...
Forum committee. He is a member of the Mathematics Association of America and on the editorial board of a new interdisciplinary journal, the International Journal of Biological Systems. He was also guest editor of the journal FORMA for a special issue on the Golden Mean
Golden mean
Golden mean may refer to:*Doctrine of the Golden Mean , a chapter in Li Ji, one of the Four Books of Confucianism*Golden mean , the felicitous middle between the extremes of excess and deficiency...
in 2005.
Selected bibliography
- Kappraff, J. “Ancient Harmonic Law.” Bridges 2007. (2007)
- Kappraff, J. “The Lost Harmonic Law of the Bible.” Proceedings of London-Bridges 2006. Edited by J. Sharp.
- Kappraff, J. and McClain, E.G. “The Proportions of the Parthenon: A work of musically inspired architecture” International Journal for Music Iconography, Vol. XXX, no. 1–2 Spring–Fall 2005
- Kappraff, J. In Search of the Golden Mean. FORMA Vol. 19, No. 4 (2005)
- Kappraff, J. Growth of Plants: A Study in Number. FORMA Vol 19, No. 4 (2005).
- Kappraff, J. and Adamson, G.W. Generalized Binet Formulas, Lucas Polynomials, and Cyclic Constants. FORMA vol. 19, No. 4 (2005)
- Kappraff, J., Jablan, S., Adamson, G.W., Sazdonovich, R. Golden Fields, Generalized Fibonacci Sequences, and Chaotic Matrices. FORMA vol. 19, No. 4 (2005).
- Kappraff, J. and Adamson, G.W. Polygons and Chaos. Journal of Biological Systems and Geometric Theories, Vol. 2 pp 79–94 (Nov. 2004).
- Kappraff, J. The Anatomy of a Bud. In Bridges:2004 edited by R. Sarhangi. Winfield,KS:Central Plains books (2004)
- Kappraff, J. and Adamson, G.W. The Relationship of the Cotangent Function to Special Relativity Theory, Silver Means, p-cycles, and Chaos Theory. FORMA. Vol.18, No. 3 pp 249–262 (2003)
- Kappraff, J. The Anatomy of a Bud. In Bridges:2004 edited by R. Sarhangi. Winfield,KS:Central Plains books (2004)
- Kappraff, J. and Adamson, G.W. Polygons and Chaos. Journal of Dynamical Systems and Geometric Theories, Vol. 2 pp 79–94 (Nov. 2004).
- Kappraff, J. Complexity and Chaos Theory in Art. Chaos and Complexity Letters, Vol 3.. Special Issue on Chaos and Complexity in Arts and Architecture. In press.
- Kappraff, J. and McClain,E. The System of Proportions of the Parthenon: A Work of Musically Inspired Architecture. Music in Art: International Journal of Music Iconography. In press.
- Kappraff, J and Adamson, G.W. A Unified Theory of Proportion. Conference Proceedings of ISAMA-Bridges 2003. J. Barrallo, et. al. editors (2003) and in Journal of Visual Mathematics
- Kappraff, J. “The System of Proportions of the Parthenon and its Meaning.” Proceedings of the 5th Bridges Conference, ed. by R. Sarhangi (2002).
- Kappraff and Adamson, G.W. “Polygons and Chaos.” Symmetry : Art and Science No. 1/2 (2001).
- Kappraff, J. “Beyond Measure: Essays in Nature Myth, and Number.” 600 pages., Singapore: World Scientific In press. (2002)
- Kappraff, J. "A Secret of Ancient Geometry." In Geometry at, Work edited by C.Gorini. Mathematics Association of American Geometry MAA Notes No. 53 (2000)
- Kappraff, J. and Hawkins, G. “The Music of the Spheres: Was Kepler Wrong?” unpublished.
- Kappraff, J. and Adamson, G.W. “A Fresh Look at Number.” Visual Mathematics (an electronic journal, Vol. 2, No. 3 Fall 2000.
- Kappraff, J. “The Arithmetic of Nicomachus of Gerasa and its Applications to Systems of Proportion” Nexus Network Journal Vol. 4, No. 3 October 2000.
- Kappraff, J. “The Hidden Pavements of Michelangelo’s Laurentian Library.” Article in the Mathematical Tourist section of Mathematical Intelligencer. June 1999.
- Kappraff, J. “Systems of Proportion in Design and Architecture and their relationship to Dynamical Systems.” In Visual Mathematics (an electronic journal). Issue 1. Feb. 1999.
- Kappraff, J., Blackmore, D., and Adamson, G. "Phyllotaxis asDynamical System: A Study in Number." In Symmetry in Plants edited by R.V. Jean and D. Barabe. Singapore: World Scientific. In print (1996).
- Kappraff, J. "Musical Proportions at the Basis of Architectural Proportions both Ancient and Modern." In Nexus '96 edited by K. Williams. Fuccechio: Edizioni Dell' Erba. In print (1996).
- Kappraff, J. "Linking the Musical Proportions of Renaissance, the Modulor, and Roman Systems of Proportions." Space Structures, Vol. 11, Nos. 1 and 2 (1996).
- Blackmore, D. and Kappraff, J. "Phyllotaxis and Toral Dynamical Systems." Journal of Applied Mathematics and MechanicsJournal of Applied Mathematics and MechanicsThe Journal of Applied Mathematics and Mechanics, also known as Zeitschrift für Angewandte Mathematik und Mechanik or ZAMM is a peer-reviewed academic journal dedicated to applied mathematics, the journal of the Gesellschaft für Angewandte Mathematik und Mechanik...
(1995). - Kappraff, J. "Tangrams, Amish Quilts, and Sacred Geometry". SIAM Newletter in Discrete Mathematics. May 1993.
- Kappraff, J. "Connections: The Geometric Bridge between Art and Science " 470 pages. New York: McGraw–Hill. 1991.
- Kappraff, J. "The Relationship between Mathematics and Mysticism of the Golden Mean through History." In Five-fold Symmetry in a Cultural Context edited by Istvan Hargittai. Singapore: World Scientific. 1991.
- Kappraff, J. "The Spiral in Myth, Mathematics, and Nature." In Spiral Symmetry edited by I. Hargittai and C.A. Pickover. Singapore:World Scientific. 1991.
- Kappraff, J. "A Course in the Mathematics of Design." In Symmetry:Unifying Human Understanding. Edited by I. Hargittai. Pergamon Press. 1986.
- Kappraff, J. "The Geometry of Coastlines: A study in Fractals." In Symmetry: Unifying Human Understanding edited by I. Hargittai. Pergamon Press. 1986.