Summary: A result of Archimedes states that for perpendicular chords passing through a point P in the interior of the unit circle, the sum of the squares of the lengths of the chord segments from P to the circle is equal to 4. A generalization of this result to (Formula presented.) chords is given. This is done in the backdrop of revisiting Problem 1325 from Crux Mathematicorum, for which a new solution is presented
AbstractThe chords’ problem is a variant of an old problem of computational geometry: given a set of...
Many problems in combinatorial geometry can be formulated in terms of curves or surfaces containing ...
Title: Trisection of an angle and duplicity of the cube by means of special curves Author: Jan Kozub...
Problem. Through the midpoint P of a chord of a circle, any two chords, AB and CD, are drawn. If AD ...
A famous theorem in Euclidean geometry often attributed to the Greek thinker Pythagoras of Samos (6t...
who loved Ptomeny’s Theorem. Ptolemy’s Theorem is a beautiful, classical result concerning quadrilat...
In this article, we explore a proof involving two vertical chords in a circle that are perpendicular...
Let ABC be a triangle. Let A'A'', B'B'', and C'C'' be tangents to the incircle of ABC and parallel t...
The chords’ problem is a variant of an old problem of computational geometry: given a set of points ...
Plane GeometryLet the chord CF intersect the diameter AB of a circle. Let D and E be the feet of the...
Carnot's theorem states that the signed sum of the perpendicular distances from the circumcenter of ...
Carnot's theorem states that the signed sum of the perpendicular distances from the circumcenter of ...
In this work, we identify some traces of the history of Archimedes’ straight line, a lemma introduce...
Plane GeometryLet the chord CF intersect the diameter AB of a circle. Let D and E be the feet of the...
Let ABC be a triangle. Let A'A'', B'B'', and C'C'' be tangents to the incircle of ABC and parallel t...
AbstractThe chords’ problem is a variant of an old problem of computational geometry: given a set of...
Many problems in combinatorial geometry can be formulated in terms of curves or surfaces containing ...
Title: Trisection of an angle and duplicity of the cube by means of special curves Author: Jan Kozub...
Problem. Through the midpoint P of a chord of a circle, any two chords, AB and CD, are drawn. If AD ...
A famous theorem in Euclidean geometry often attributed to the Greek thinker Pythagoras of Samos (6t...
who loved Ptomeny’s Theorem. Ptolemy’s Theorem is a beautiful, classical result concerning quadrilat...
In this article, we explore a proof involving two vertical chords in a circle that are perpendicular...
Let ABC be a triangle. Let A'A'', B'B'', and C'C'' be tangents to the incircle of ABC and parallel t...
The chords’ problem is a variant of an old problem of computational geometry: given a set of points ...
Plane GeometryLet the chord CF intersect the diameter AB of a circle. Let D and E be the feet of the...
Carnot's theorem states that the signed sum of the perpendicular distances from the circumcenter of ...
Carnot's theorem states that the signed sum of the perpendicular distances from the circumcenter of ...
In this work, we identify some traces of the history of Archimedes’ straight line, a lemma introduce...
Plane GeometryLet the chord CF intersect the diameter AB of a circle. Let D and E be the feet of the...
Let ABC be a triangle. Let A'A'', B'B'', and C'C'' be tangents to the incircle of ABC and parallel t...
AbstractThe chords’ problem is a variant of an old problem of computational geometry: given a set of...
Many problems in combinatorial geometry can be formulated in terms of curves or surfaces containing ...
Title: Trisection of an angle and duplicity of the cube by means of special curves Author: Jan Kozub...
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