plane geometry, Apollonius's problem is to construct circles that are tangent to three given circles in a plane (Figure 1). Apollonius of Perga (c. 262...

(2007), "The tangency problem of Apollonius: three looks" (PDF), BSHM Bulletin: Journal of the British Society for the History of Mathematics, 22 (1):...

plan from Apollonius himself, who visited Pergamon, Eudemus insisted Apollonius send him each book before release. At this stage Apollonius was likely...

ratio of distances to the other two. The isodynamic points and Lemoine line of a triangle can be solved using these circles of Apollonius. Apollonius' problem...

on Apollonius' Theorem". Resource Notes. Mathematics in School. 36 (5): 24–25. JSTOR 30216074. Stokes, G. D. C. (1929). "The theorem of Apollonius by...

(rule and compass) of the lost answer to the problem first set by Apollonius of Perga. Van Roomen could not overcome that problem without resorting to...

and a conceptual solution of the problem of Apollonius. Lie sphere geometry can be defined in any dimension, but the case of the plane and 3-dimensional...

geometry, Apollonius' problem is to construct all the circles that are tangent to three given circles. Special cases of Apollonius' problem are those...

up Apollonius in Wiktionary, the free dictionary. Apollonius (Ancient Greek: Άπολλώνιος) is a masculine given name which may refer to: Apollonius of Athens...

The problem of Apollonius is one of the earliest examples of enumerative geometry. This problem asks for the number and construction of circles that are...

Systems of mutually tangent circles were studied by Apollonius of Perga, after whom the problem of Apollonius and the Apollonian gasket are named. In the 17th...

the circle is a problem in geometry first proposed in Greek mathematics. It is the challenge of constructing a square with the area of a given circle by...

Apollonius of Perga, Euclid is generally considered among the greatest mathematicians of antiquity, and one of the most influential in the history of...

quadrilaterals Problem of Apollonius Recreational mathematics Seki Takakazu Holly, Jan E.; Krumm, David (2020-07-25). "Morikawa's Unsolved Problem". arXiv:2008...

the Problem of Apollonius Construction of the Malfatti circles: For a given triangle determine three circles, which touch each other and two sides of the...

texts of Euclid, Archimedes, Apollonius, and Pappus in particular went on to influence the development of early modern mathematics. Some problems in Ancient...

Apollonius of Rhodes (Ancient Greek: Ἀπολλώνιος Ῥόδιος Apollṓnios Rhódios; Latin: Apollonius Rhodius; fl. first half of 3rd century BC) was an ancient...

solution of the Apollonius problem has been known for centuries. But the Apollonius point was first noted in 1987. The Apollonius point of a triangle...

heavenly ascension. Most modern scholars of antiquity agree that Apollonius existed historically. Apollonius was born into a respected and wealthy aristocratic...

problem briefly in 1643, in two letters to Princess Elisabeth of the Palatinate. Descartes initially posed to the princess the problem of Apollonius....

determined by its three tangencies. Constructing it is a special case of the Problem of Apollonius. Alternative approaches to constructing two circles congruent...

trigonometry and geometry; and on the decimal expansion of pi. He solved the Problem of Apollonius using a new method that involved intersecting hyperbolas...

"hobby" himself). He published a number of translations of major works of Euclid, Archimedes, Apollonius of Perga and others; most are still used today...

novel solution to the following three-dimensional extension of the problem of Apollonius: Construct all possible spheres that are simultaneously tangent...

Lester's theorem Problem of Apollonius Whitworth, William Allen (1866). Trilinear Coordinates and Other Methods of Modern Analytical Geometry of Two Dimensions...

positive views of him. He rediscovered the Descartes' theorem in 1936 and published it as a poem, "The Kiss Precise", quoted at Problem of Apollonius. The kissing...

role in his solution of the problem of Apollonius. In planar dynamics a pole is a center of rotation, the polar is the force line of action and the conic...

mathematician Apollonius, who asked how many circles in the plane are tangent to three given circles. In general, the solution to the problem of Apollonius is that...

planes. Homothetic centers of circles Problem of Apollonius Wells, David (1991). The Penguin Dictionary of Curious and Interesting Geometry. New York: Penguin...

proponent of the techniques of analytical geometry and in 1814, he devised an elegant coordinate solution to the classical problem of Apollonius: to find...