MATHEMATICAL TRIPS

Invitations, in an educational vein, to problem solving, ideas and their history, biographical snapshots, visuals, classroom capsules, undergraduate research ideas, recreations, experiments, arts and poetry, philosophical and foundational matters and connections.

Thursday, February 26, 2015

Roger Penrose lecture at Penn State: Faith, Fashion, and Fantasy: How Big is Infinity?

Posted by Mihai Caragiu
Email ThisBlogThis!Share to TwitterShare to FacebookShare to Pinterest
Labels: geometry, mathematical physics, physics/cosmology, Roger Penrose, science, science news
Newer Posts Older Posts Home
Subscribe to: Posts (Atom)

@ONUMathStat

Tweets by @ONUMathStat

The ever Intriguing Euler-Fibonacci sequence

Introduced by Mihai Caragiu in 2010, the Euler-Fibonacci sequence was the theme in the undergraduate research project which resulted in the May 2011 publication Mihai Caragiu and Ashley Risch, An Euler-Fibonacci Sequence, Far East Journal of Mathematical Sciences 52 (1), 1 - 7. The image below displays the quotients of consecutive terms.


And here are the first couple of terms (for more, click here): 1, 1, 2, 2, 4, 6, 10, 16, 18, 24, 42, 66, 108, 120, 228, 348, 576, 720, 1296, 2016, 3312, 5256, 7200, 12456, 17860, 25200, 40256, 37368, 39600, 72900, 112500, 185400, 282204, 364800, 517600, 805392, 1133988, 1939380, 2788176, 4727556, 6819120, 11539840, 18324852, 28220080, 46471680, 70297856, 77663160, 98640672, 173595168, 256221952, 408844800, 613907760, 1020322800, 1598868000, 2614401972, 3650502240, 6204873360, 9219832128, 14163287040, 23375208496, 37533203556, 59869153008, 77921885248, 136242824256, 171331767600, 280988047872, 412648088320, 492483317760, 759235553856, 1248565926960, 1825274073460, 3073836307872, 3978113132448, 6636847261248, 9414599018400,...

Blog Archive

  • ►  2018 (2)
    • ►  February (2)
  • ►  2017 (8)
    • ►  September (1)
    • ►  August (6)
    • ►  April (1)
  • ►  2016 (10)
    • ►  November (1)
    • ►  March (5)
    • ►  February (1)
    • ►  January (3)
  • ▼  2015 (26)
    • ►  December (6)
    • ►  November (2)
    • ►  October (1)
    • ►  September (2)
    • ►  August (1)
    • ►  July (5)
    • ►  June (1)
    • ►  March (5)
    • ▼  February (1)
      • Roger Penrose lecture at Penn State: Faith, Fashio...
    • ►  January (2)
  • ►  2014 (25)
    • ►  December (4)
    • ►  November (6)
    • ►  September (3)
    • ►  August (3)
    • ►  July (1)
    • ►  June (1)
    • ►  May (1)
    • ►  April (1)
    • ►  March (4)
    • ►  February (1)
  • ►  2013 (25)
    • ►  December (5)
    • ►  November (3)
    • ►  September (1)
    • ►  August (2)
    • ►  July (2)
    • ►  June (1)
    • ►  May (1)
    • ►  April (2)
    • ►  February (2)
    • ►  January (6)
  • ►  2012 (20)
    • ►  December (2)
    • ►  November (3)
    • ►  October (3)
    • ►  September (1)
    • ►  August (1)
    • ►  July (1)
    • ►  June (4)
    • ►  May (1)
    • ►  April (1)
    • ►  February (1)
    • ►  January (2)
  • ►  2011 (53)
    • ►  December (3)
    • ►  November (3)
    • ►  October (1)
    • ►  September (3)
    • ►  August (7)
    • ►  July (4)
    • ►  June (5)
    • ►  May (14)
    • ►  April (2)
    • ►  March (4)
    • ►  February (3)
    • ►  January (4)
  • ►  2010 (43)
    • ►  December (2)
    • ►  November (2)
    • ►  October (3)
    • ►  September (1)
    • ►  August (7)
    • ►  July (8)
    • ►  June (4)
    • ►  May (4)
    • ►  April (4)
    • ►  March (2)
    • ►  February (4)
    • ►  January (2)
  • ►  2009 (42)
    • ►  December (2)
    • ►  November (2)
    • ►  October (5)
    • ►  September (2)
    • ►  August (3)
    • ►  July (5)
    • ►  June (3)
    • ►  May (2)
    • ►  April (2)
    • ►  March (2)
    • ►  February (6)
    • ►  January (8)

About Me

My photo
Mihai Caragiu
B.Sc. 1987 and M.Sc. 1988 (Mathematics, University of Bucharest); Ph.D. 1996 (Mathematics, Pennsylvania State University). Professor of Mathematics at Ohio Northern University (my blogs do not, however, purport to express in any way the opinions of Ohio Northern University).
View my complete profile

Links

  • A Beginner's Guide to Forcing
  • A Cheerful Introduction to Forcing and the Continuum Hypothesis
  • An Introduction to p-adic Numbers and p-adic Analysis
  • Art of Problem Solving
  • Berkeley Math Circle
  • Bibliothèque nationale de France
  • Bridges conferences on art and mathematics
  • Cellule de Coordination Documentaire Nationale pour les Mathématiques
  • Centre de diffusion de revues académiques mathématiques
  • Continuous Nowhere Differentiable Functions
  • Descriptive set theory lecture notes
  • Dirichlet's Theorem on primes in arithmetic progressions
  • Dr. Vogel's Gallery of Calculus Pathologies
  • Earliest Known Uses of Some of the Words of Mathematics
  • Engaging Students through the History of Mathematics
  • Euclid Elements
  • Extended Euclidean Algorithm applet
  • Factoring applet also providing the Euler and Carmichael functions
  • Factoris
  • Factorization using the Elliptic Curve Method
  • Fast Exponentiation applet
  • Fibonacci Numbers
  • Fibonacci and Stock Market
  • Formalized Mathematics - John Harrison
  • GoGeometry.com
  • Green - Tao Ann. Math. article
  • Hilbert's Mathematical Problems
  • ICM 2010, Hyderabad, India
  • INTEGERS e-Journal (Combinatorial Number Theory)
  • Java Applets on Mathematics
  • Lectures on Spectral Graph Theory
  • Logic Matters
  • Loren on the Art of MATLAB
  • MATEFORUM.RO
  • Math Pages
  • MathPro Press
  • Mathematical Miniatures
  • Mathematicians of the day
  • Mathematics and Christianity
  • Mihailescu's proof of Catalan's Conjecture
  • Motion Mountain - The Adventure of Physics
  • Noncommutative Geometry - Alain Connes
  • Number Theory Applets
  • Number Theory Web
  • Open Problem Garden
  • Open problems in topology
  • Opinions - Doron Zeilberger
  • Perspectives on Undergraduate Research and Mentoring
  • Plouffe's Inverter
  • Portail Documentaire Mathématique - Mathdoc
  • Problems in Elementary Number Theory
  • Project Euclid - mathematics and statistics resources online
  • Recherche et téléchargement d’archives de revues mathématiques numérisées
  • Revista "Recreatii matematice"
  • Russian mathematician rejects $1 million prize
  • SCImago Journal & Country Rank
  • The "3n+1" problem
  • The On-Line Encyclopedia of Integer Sequences
  • Theorem of the Day
  • This Week's Finds in Mathematical Physics
  • Visual Cryptography
  • W3C Math Home
  • Wolfram|Alpha
  • arXiv
  • calculus.org
  • fibonacci-numbers.com
  • olimpiade.ro
  • online calculator
The question for the ultimate foundations and the ultimate meaning of mathematics remains open; we do not know in which direction it will find its final solution nor even whether a final objective answer can be expected at all. "Mathematizing" may well be a creative activity of man, like language or music, of primary originality, whose historical decisions defy complete objective rationalization. — Hermann Weyl, Gesammelte Abhandlungen

Ramanujan's series for π

blogroll

  • Mathematics - Stack Exchange
  • MathOverflow
  • Intersections -- Poetry with Mathematics
  • News from the world of maths
  • Terence Tao
  • Loren on the Art of MATLAB
  • Peter Cameron's Blog
  • The n-Category Café
  • Low Dimensional Topology
  • RO-THEORIA
  • Disquisitiones Mathematicae
  • Noncommutative geometry
  • neverendingbooks
  • Secret Blogging Seminar
  • Florin Caragiu
  • Mathematics and Multimedia
  • Explaining mathematics
  • Gowers's Weblog
  • Mathematics Education Research Blog
  • XOR's Hammer
  • On-Screen Scientist
  • Turing Finance
  • Climbing Mount Bourbaki
  • The Math Paige
  • Mathematics in Australia
  • Possibly Philosophy
  • Republic of Mathematics

APOD

Loading...

Math Genealogy Project

The Mathematics Genealogy Project
Simple theme. Powered by Blogger.