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

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

The same procedure can be followed for the other Platonic solids: Descartes's theorem on the "total defect" of a polyhedron states that if the polyhedron...

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

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

Prize Descartes' theorem (4 tangent circles) Descartes' theorem on total angular defect Folium of Descartes List of things named after René Descartes Paris...

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...

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

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

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...

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...

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...

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

circles Feuerbach's theorem on the tangency of the nine-point circle of a triangle with its incircle and excircles Descartes' theorem Ford circle Bankoff...

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...

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

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

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...

term imaginary number by René Descartes; it was meant to be derogatory. 1643 – René Descartes develops Descartes' theorem. 1654 – Blaise Pascal and Pierre...

the angle defect can be used to compute the number of vertices. Descartes' theorem states that all the angle defects in a topological sphere must sum...

{\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 (...

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...

Mohr–Mascheroni theorem Poncelet–Steiner theorem Descartes' theorem Dinostratus' theorem Dividing a circle into areas Equal incircles theorem Five circles theorem Gauss...

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

Desargues's theorem (projective geometry) Descartes's theorem (plane geometry) Descartes's theorem on total angular defect (polyhedra) Diaconescu's theorem (mathematical...

{\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...

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

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