Famous figures
Portraits of famous mathematicians, historical and contemporary
Fractals in film: from geometry to special effects
Fractal geometry was central to the earliest computer-generated imagery on the big screen. The study of self-similar forms found in nature gave rise to the first computer-generated images… and thus spawned an entire entertainment industry!
Mathematical calligrams | Tangente Magazine
A calligram is a poem arranged on the page to form an image, usually related to its subject. Here we present several quotations about mathematics in the form of calligrams.
Holiday geometry | Tangente Magazine
The holidays are also a chance to uncover the mathematics all around us
Raymond Smullyan (1919–2017): logician and magician
An eclectic mathematician, Raymond Smullyan, who died last June, was best known to the general public for his books of mathematical recreations centered on logic.
Tangente Awards
The Tangente Awards were launched to celebrate creativity inspired by mathematics and its links with many other fields, including literature, computing and the arts. Run by the Club Tangente association, these initiatives invite our readers to take part or vote at this time each year.
Paul Erdős and the probabilistic view of arithmetic
With the development of probability theory in the early 20th century, a new field of inquiry opened up in arithmetic: the statistical study of integers. Paul Erdős was among the first mathematicians to grasp the significance of this new approach.
Chinese remainder theorem: history and applications | Tangente
The Chinese remainder theorem owes its name to ancient Chinese mathematicians’ interest in the arrangement problems it describes. Originally a source of puzzles, it has since found more practical applications, particularly in cryptography.
A logarithm beneath the hyperbola | Tangente Magazine
Although Napier introduced them purely as an aid to calculation, logarithms gradually permeated every branch of mathematics. Their fundamental nature emerged particularly clearly through their connections with geometry, trigonometry and the hyperbola.
Logarithms come to the table | Tangente Magazine
I'm speaking of a time that those under twenty cannot know...
Jean-Pierre Kahane: A committed mathematician
Jean-Pierre Kahane, who passed away last June at the age of 90, left his mark on his era in many ways: through his work in analysis, which earned him international renown and election to the Académie des sciences; and through his commitment, both political and in the popularization of mathematics.
The inverse of the exponential function
The introduction of logarithms can be traced back to the Renaissance, when they were used to solve computational problems. They have since found more theoretical applications and today even lie at the heart of some cryptographic systems—and hence of our computers.
John Napier's astonishing inventions
John Napier of Merchiston, the Scottish gentleman whose death four centuries ago is being commemorated this year, was no revolutionary. Yet his wondrous invention of logarithms made him one, opening up a new world for mathematics far beyond computation.
What names for the complex numbers? | Tangente
Imaginary numbers were already introduced by the Italian mathematician Girolamo Cardano in 1545, though they did not yet have a name at the time; their first formalization is due to his compatriot Rafaele Bombelli in 1572.
The zeta function and the Riemann hypothesis
The most important problem in contemporary mathematics can be stated in entirely elementary terms, requiring only a rudimentary knowledge of complex analysis. Despite mathematicians' titanic efforts, the Riemann hypothesis remains stubbornly out of reach.
The complex exponential
How can the classical exponential function be extended to complex numbers? Will its usual properties be preserved? Although the resulting extension is easy to study, the associated notion of a complex logarithm is more elusive. It was the subject of controversy in the 18th century.
Complex numbers and trigonometry
The link between the exponential function and the familiar trigonometric functions is well known to anyone who has studied mathematics. Less well known is that this relationship extends to hyperbolic functions, which are useful in electrical engineering!
Poincaré, geometry and robotics | Tangente
Mathematics, and geometry in particular, is an essential component of that most technical of fields: robotics. The concept of space, which the mathematician Henri Poincaré (1854–1912) explored in depth, lies at the heart of the robotics engineer's work.
Pascal's triangle: a thousand-year history | Tangente
"Pascal's triangle" may have been discovered by Indians more than two thousand years ago. It reached the Arab-Muslim world and China as early as the 11th century. It did not appear in Europe until the 16th century, when Blaise Pascal began to study it rigorously.
Those equation fanatics who created imaginary numbers
Complex numbers, initially termed "imaginary," were not conceived as we study them today. Above all, they were introduced as tools for solving polynomial equations—and tackling the mathematical challenges that raged across Renaissance Europe.
Pascal's triangle, programming and Fourier | Tangente
Rich in countless combinatorial and numerical properties, Pascal's triangle is ubiquitous in mathematics. Some of its applications in analysis, however, remain little known. The capabilities of the fx-CP400+E computer algebra calculator suggest a signal-processing activity.