Mathematical Themes
Explore the major mathematical themes: geometry, algebra, analysis, arithmetic, logic, and many other fascinating fields.
What's new in the International System of Units | Tangente
The 27th General Conference on Weights and Measures was held in November in Versailles (Yvelines). Participants were delegates from the states that had signed the Metre Convention.
The football World Cup's "8" | Tangente
Despite its Möbius-strip appearance, the logo of the 2022 FIFA World Cup is simply an "8".
Geometric puzzles at infinity
Some of the most famous sangaku figures echo other mathematical constructions, forging beautiful connections between results established in different places and at different times. Here is a particularly striking example.
The golden ratio in sangaku
Though Western in origin, the golden ratio is said to be everywhere. So we went looking for it in sangaku… and struggled to find it, except in a few rare figures. But perhaps we simply overlooked it!
The barber was a woman
The barber paradox is said to be just the thing for dazzling people at parties. Although it serves an educational purpose by illustrating one of the most fundamental results in set theory, taken out of context it may well backfire on you!
The last two sangaku solved | Tangente
Of all the sangaku on record, two have proved particularly difficult to solve. The Japanese mathematician Yamaguchi Kanzan (c. 1781–1850) collected them in his travel journal between 1817 and 1828.
A passion for Goldbach's conjecture | Tangente
In set theory, which Cantor founded, intuition has little place. Yet his approach to open mathematical problems relied more on intuition than on rigorous reasoning. His interest in Goldbach's conjecture is a case in point.
Geometry theorems
With the country cut off almost entirely from the world during the Edo period, Japanese mathematics developed in isolation for more than a century and a half. It was during this period that highly distinctive geometric puzzles flourished and prospered.
Cantor−Bernstein:
Georg Cantor left his mark on the history of mathematics through his study of infinite sets. The Cantor–Bernstein theorem shows how a few results that are obvious for finite sets generalize to infinite sets… provided one takes a serious look at the question.
A journey into infinity | Tangente
While many mathematicians toiled in the footsteps of their predecessors, Cantor opened up an entirely new field that many of his colleagues refused to enter. This journey through the different infinities proved to be both fascinating and fruitful.
Editorial
"Tangente", from the Latin tangere, "to touch". If it's the name of your favorite magazine, it is because the word is rich in meanings that have opened up entire branches of mathematics.
Catriona Agg's geometry puzzles | Tangente
Catriona Agg (until recently also known as Catriona Shearer) is a British mathematics teacher from Cambridge.
The origins of the tangent
“Tangent” is a word that has found its way into everyday language. But where did it come from?
Envelope of a parametrized family of lines | Tangente
Using tangency, a family of lines can also define a curve.
A remarkable line: the asymptote
A look back at some properties of asymptotes...
Tangents and derivatives
For many people, tangents and derivatives go hand in hand.
The beautiful geometry of sangaku
A sangaku was originally a Japanese wooden votive tablet. It sometimes bears an engraved geometric figure with the statement of a problem, together with the solution or sometimes a hint.
Constructing tangents
If we know how to carry out the classic straightedge-and-compass constructions, we are perhaps less at ease drawing the common tangents to two circles. Now is the time to put our whole range of knowledge of Euclidean geometry into practice!
The revenge of the tangent spheres in 4D | Tangente
By shedding new light on the semiregular polyhedra of space, Alicia Boole Stott's method makes it possible to go further and explore objects in the fourth dimension. In particular, she was able to set out in search of semiregular polytopes.
Curves made of straight lines: string art | Tangente
String pictures—decorative designs drawn or made with thread or cord—enjoyed their heyday around 1975. Today they are back in fashion under the name string art.