
Discover the Fascinating World of Euclidean Geometry: Explore Classical Theorems and Their Applications Today!
Lines stretch infinitely,
Circles embrace symmetry,
Angles speak their truth.
Geometry's timeless grace,
A testament to our world.
Classical geometry is a branch of mathematics that deals
with the study of geometry based on Euclid's Elements.
Euclid's Elements is a widely influential book in mathematics
that lays out a comprehensive system of geometry that has been
studied for thousands of years. Classical geometry is
concerned with the study of points, lines, and shapes in two
and three dimensions, as well as their relationships and
properties. Classical geometry has many applications in fields
such as architecture, engineering, physics, and computer
graphics.
This index includes definitions, formulas,
and interactive illustrations to help users understand and
explore each theorem. It is a useful resource for students,
teachers, and anyone interested in mathematics and geometry.


Classical Theorems  Page 1


Dynamic Geometry 1478.
Cyclocevian, ReuschleTerquem Theorem, Concurrent Cevians, Triangle, Circumcircle, Secant line, Stepbystep Illustration. GeoGebra,
iPad. 

Dynamic Geometry 1477.
Miquel's Pentagram Theorem, Pentagon, Triangle, Circumcircles, Concyclic Points, Stepbystep Illustration. GeoGebra,
iPad. 

Dynamic Geometry 1476.
DrozFarny Line Theorem, Triangle, Orthocenter, Perpendicular, Collinear Midpoints, Stepbystep Illustration. GeoGebra,
iPad. 

Dynamic Geometry 1475.
Clifford Intersecting Circles Theorem, Stepbystep Illustration, GeoGebra, iPad. 

Dynamic Geometry 1474.
Butterfly Theorem, Circle, Chords, Midpoints, Stepbystep Illustration. 

Dynamic Geometry 1473.
Kosnita's Theorem, Triangle, Four Circumcenters, Concurrent Line, Stepbystep Illustration. 

Dynamic Geometry 1468.
Steiner's Theorem, Triangle, Circumradius, Inradius, Sum of Exradii, Stepbystep Illustration. 

Geometry Problem 1466.
Tangential Quadrilateral, Newton Line, Incenter, Midpoint, Diagonal, Collinear Points.
Stepbystep Illustration using GeoGebra. 

Geometry Problem 1462.
NewtonLine, NewtonGauss Line, Complete Quadrilateral, Midpoints of Sides and Diagonals,
Collinear Points. Stepbystep Illustration using GeoGebra. 

Dynamic Geometry
1460.
NewtonGauss Line, Complete Quadrilateral, Midpoints of Diagonals,
Collinear Points, Stepbystep Illustration using GeoGebra. 

Geometry
Problem 1455.
Nagel Point, Excircles, Incircle, Congruent Segments,
iPad. Stepbystep illustration using GeoGebra. 

Dynamic Geometry 1452.
Japanese Theorem, Sangaku,
Cyclic Quadrilateral, Incenter, Rectangle, Inradius. Stepbystep
illustration using GeoGebra. 

Dynamic Geometry 1451.
Orthopole of a Line. Stepbystep
illustration using GeoGebra. 

Dynamic Geometry 1450.
Ortholine, Steiner Line, Complete Quadrilateral, Collineal Orthocenters. Stepbystep
illustration using GeoGebra. 

Dynamic Geometry 1449.
Salmon Line. Stepbystep
illustration using GeoGebra. 

Dynamic Geometry 1448.
Simson Line. Stepbystep
illustration using GeoGebra. 

Dynamic Geometry Problem 1447.
Outer Vecten Point. Stepbystep
illustration using GeoGebra. 

Dynamic Geometry Problem 1446.
Lemoine Line, triangle, circumcircle, tangent, collinear points. Stepbystep animation using GeoGebra. 

Dynamic Geometry Problem 1444.
The Asymmetric Propeller Theorem, Equilateral Triangles, Midpoints. Stepbystep animation using GeoGebra. 

Pythagorean Theorem.


Euclid's Elements Book II, Proposition 12: Law of Cosines.


Euclid's Elements Book II, Proposition 13: Law of Cosines.


Median
length, Apollonius' Theorem 

The significance of the Pythagorean theorem by Jacob
Bronowski.
Pythagorean Theorem, 47th Proposition of Euclid's Book I. 

Carnot's Theorem. Geometry Problem 889
Carnot's Theorem in an acute triangle, Circumcenter, Circumradius, Inradius. GeoGebra, HTML5 Animation for Tablets. 

Ceva's Theorem.
Concurrency. Interactive proof with animation. Key concept:
Menelaus Theorem. 

Menelaus' Theorem. Interactive proof with
animation and key concepts..


van Aubel's Theorem.
Quadrilateral with Squares. Proof with animation. 

van Aubel's Theorem.
Quadrilateral with Squares. Proof with animation for Tablets, iPad,
Nexus, Galaxy. 

Dynamic Geometry Problem 1445.
Van Aubel's theorem, Quadrilateral and Four Squares, Centers. Stepbystep animation using GeoGebra. 

Heron's Formula.
Key facts and
a purely geometric
stepbystep proof.


Euclid's Elements
Book I, 23 Definitions. Onepage visual illustration.
Euclid's Elements Book.
Index 

Euclid's Elements Book VI, Proposition 3: Angle Bisector Theorem 

Euclid's
Elements, Book XIII, Proposition 10 One page visual illustration. 

Ptolemy's Theorem.


Dynamic Geometry: Brahmagupta Theorem,
. GeoGebra, HTML5 Animation for Tablets 

Brianchon's Theorem in a Circumscribed Hexagon. 

Brianchon Corollary, Circumscribed Hexagon, Concurrency lines. 

Carnot's
Theorem in an Acute Triangle. 

Carnot's
Theorem in an Obtuse Triangle. 

Clifford's Circle Chain
Theorems. This is a step by step presentation of the first theorem.
Clifford discovered, in the ordinary Euclidean plane, a "sequence or
chain of theorems" of increasing complexity, each building on the last
in a natural progression.


Cyclic
Quadrilateral: Ratio of the Diagonals


NinePoint Center, NinePoint Circle, Euler Line.
Interactive illustration.


Soddy
Circles and Descartes Theorem.
Three tangent circles, Inscribed and Circumscribed Circles, Radii. 

Euler's Problem, Problem 155. Distance between the Incenter to the Circumcenter. 

The Simson Line, Theorems
and Problems  Index. 

Casey's Theorem. Generalized Ptolemy's Theorem.


Brahmagupta's Formula
Area of a cyclic quadrilateral.


Brahmagupta's Theorem
Cyclic quadrilateral.


Platonic
Solids, Interactive animation.
HTML5 Animation for iPad and Nexus
Flash Animation. 

Theaetetus' Theorem, Platonic Solids, Interactive animation 
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Last updated: Jun 14, 2023





