In geometry, Descartes' theorem states that for every four kissing, or mutually tangent circles, the radii of the circles satisfy a certain quadratic equation...

Descartes' theorem states that, for every four mutually tangent circles, the radii of the circles satisfy a certain quadratic equation. Descartes' theorem...

every vertex in the polyhedron. A converse to Descartes' theorem is given by Alexandrov's uniqueness theorem, according to which a metric space that is locally...

Gauss–Bonnet for smooth manifolds and Descartes' theorem. There are several combinatorial analogs of the Gauss–Bonnet theorem. We state the following one. Let...

In mathematics, Descartes' rule of signs, described by René Descartes in his La Géométrie, counts the roots of a polynomial by examining sign changes...

rule of signs Descartes-Huygens Prize Descartes' theorem (4 tangent circles) Descartes's theorem on total angular defect Folium of Descartes List of things...

attention. René Descartes gave a formula relating the radii of the solution circles and the given circles, now known as Descartes' theorem. Solving Apollonius'...

were some Jews who held positive views of him. He rediscovered the Descartes' theorem in 1936 and published it as a poem, "The Kiss Precise", quoted at...

sum of four squares with his own four-square theorem. The formula is also linked to Descartes' theorem of four "kissing circles", which involves the...

Gershgorin circle theorem Clifford's circle theorems Descartes' theorem also known as 'kissing circles' or 'Soddy circles' theorem List of circle topics...

In mathematics, the Pythagorean theorem or Pythagoras' theorem is a fundamental relation in Euclidean geometry between the three sides of a right triangle...

the general case. A discrete analog of the Gauss–Bonnet theorem is Descartes' theorem that the "total defect" of a polyhedron, measured in full circles...

polynomials. For computing over the reals, Sturm's theorem is less efficient than other methods based on Descartes' rule of signs. However, it works on every...

π/2 at each of its eight vertices. Descartes' theorem on total angular defect (a form of the Gauss–Bonnet theorem) states that the sum of the angular...

squares of the four sides to the sum of the squares of the diagonals Descartes' theorem for four kissing circles involves sums of squares The sum of the squares...

De Bruijn–Erdős theorem (incidence geometry) De Gua's theorem (geometry) Desargues's theorem (projective geometry) Descartes's theorem (plane geometry)...

Apollonian gasket are named. In the 17th century René Descartes discovered Descartes' theorem, a relationship between the reciprocals of the radii of...

expression involves finding the two solutions of a quadratic equation. Descartes' theorem states that for every four kissing (mutually tangent) circles, their...

morphisms Descartes number Descartes' rule of signs Descartes snark Descartes' theorem Descartes' theorem on total angular defect Folium of Descartes Cartesian...

theorem, albeit with the use of infinitesimals rather than derivatives.: 456–457 : 2  After Marin Mersenne passed the treatises onto René Descartes,...

solidorum elementis, Descartes states (without proof) Descartes' theorem on total angular defect, a discrete version of the Gauss–Bonnet theorem according to...

rediscovered until the 19th century. One of its contributions was Descartes' theorem on total angular defect, which is closely related to Euler's polyhedral...

{\displaystyle \delta =2\pi -q\pi \left(1-{2 \over p}\right).} By a theorem of Descartes, this is equal to 4π divided by the number of vertices (i.e. the...

of three touching circles with a common tangent, a special case of Descartes' theorem. Given the size of the two outer large circles, what is the size of...

In algebra, the rational root theorem (or rational root test, rational zero theorem, rational zero test or p/q theorem) states a constraint on rational...

Fermat scribbled his famous note about Fermat's Last theorem in his copy of Arithmetica. Descartes, working through the Problem of Apollonius from his...

{\displaystyle \#_{+}=\#_{(0,r)},} which makes Descartes' rule of signs a special case of Budan's theorem. As for Descartes' rule of signs, if v ℓ ( p ) − v r (...

circles in the pair. The size of each new circle is determined by Descartes' theorem, which states that, for any four mutually tangent circles, the radii...

polyhedra, is the (angular) defect; the analog for the Gauss–Bonnet theorem is Descartes' theorem on total angular defect. Because (Gaussian) curvature can be...

triangle. They are all named for Frederick Soddy, who rediscovered Descartes' theorem on the radii of mutually tangent quadruples of circles. Any triangle...