Surveying and measuring
Since the beginning, humans have needed to predict, and therefore to measure. How to evaluate the distance between two buildings, two cities, two mountains, two planets? The GPS integrated into our phones and our cars would almost make us forget that there was a time (not so far away) when estimating a distance was a scientific feat! This began with surveying in a nearby environment, then we became interested in distances that are directly inaccessible, allowing us to find our location on land, at sea or in space. New techniques, often relying on clever mathematics like triangulation, were imagined, as well as a whole range of challenges: finding the shortest paths, determining equidistance curves, placing points as regularly as possible on a sphere…
All articles in this folder
The point farthest from France's borders
Where is the "true" center of France? The question sometimes crops up among fans of recreational mathematics and divides enthusiasts of geographical curiosities. Depending on the criterion used to define this center, it may lie in the Cher, the Indre or… the Finistère!
Distances on a sphere: spherical geometry | Tangente
Pioneered by Menelaus of Alexandria in the first century CE, spherical geometry can be a little disconcerting. It is two-dimensional: for example, longitude and latitude are enough to locate any point on the sphere's surface.
Measuring distances in the Age of Enlightenment
In the 18th century, many mathematical treatises dealt with practical geometry. They presented numerous problems involving the measurement of lines, areas and solids, together with their solutions. Various methods were reviewed for measuring the shortest path between two points.
Equidistance curves: equidistant points | Tangente
We know how to locate points equidistant from one point, two points, or even two lines—but what about points equidistant from other geometric figures?
Where is the geographic center of France? | Tangente
What do we mean by "the" center of France?
Points on the sphere: the hostile dictators problem | Tangente
How can points be distributed "as well as possible" on a sphere? The idea is to place them "as far apart as possible." With two, three or four points, one might think that the vertices of a regular polyhedron inscribed in the sphere would do the trick. And yet…
A stroll through the solar system
How can we measure the distances between us and the various planets in the solar system? We can use a common reference unit, such as the distance from Earth to the Sun. But how can we estimate that distance? The history of these calculations stretches back at least as far as the scholars of antiquity!