Critical Thinking Mind Map

Critical Thinking is a form of judgment, specifically purposeful and reflective judgment. In using critical thinking one makes a decision or solves the problem of judging what to believe or what to do, but does so in a reflective way. Click the figure below.



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The Garden of Earthly Delights by Hieronymus Bosch

Kaleidoscope
The Garden of Earthly Delights or The Millennium is a triptych painted by the master Hieronymus Bosch (c. 1450 - 1516), housed in the Museo del Prado in Madrid since 1939.



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Elearn Geometry Problem 213: Triangle, Incircle, Inradius, Semicircles, Common Tangents

See complete Problem 213 at:
gogeometry.com/problem/p213_triangle_inradius_common_tangents.htm

Level: High School, SAT Prep, College geometry

Art Forms of Nature: Arachnid by Ernst Haeckel

Kaleidoscope
Kunstformen der Natur (German for Art Forms of Nature) is a book of lithographic and autotype prints by German biologist Ernst Haeckel.



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gogeometry.com/wonder_world/haeckel_kunstformen_arachnid_1.html

Art Forms of Nature: Ascidiae by Ernst Haeckel

Kaleidoscope
Kunstformen der Natur (German for Art Forms of Nature) is a book of lithographic and autotype prints by German biologist Ernst Haeckel.



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gogeometry.com/wonder_world/haeckel_kunstformen_ascidiae_1.html

Art Forms of Nature: Actiniae by Ernst Haeckel

Kaleidoscope
Kunstformen der Natur (German for Art Forms of Nature) is a book of lithographic and autotype prints by German biologist Ernst Haeckel.



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gogeometry.com/wonder_world/haeckel_kunstformen_actiniae_1.html

Classical Theorems

Index
Pythagorean theorem, Heron, Ptolemy, Brahmagupta, Menelaus, Ceva, Nine Point Center, Theaetetus, Euler's Polyhedron, Pascal, Pappus, van Aubel, Eyeball, Butterfly, and more.



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gogeometry.com/geometry/classical_theorems_index.html

Elearn Geometry Problem 212: 120 Degree Triangle, Areas

See complete Problem 212 at:
gogeometry.com/problem/p212_triangle_120_equilateral_area.htm

120 degrees triangle, equilateral triangle, areas. Level: High School, SAT Prep, College geometry

Bottema's Theorem: Triangle and Squares

Dynamic Geometry Software. Step-by-Step construction, Manipulation, and animation
Draw squares ABDE and BCFG on sides AB and BC of a triangle ABC. Then the midpoint M of EF is independent of B and the triangle AMC is an isosceles right triangle.



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gogeometry.com/geometry/bottema_theorem_triangle_square.htm

Archimedes' Arbelos and Square 2

Dynamic Geometry Software. Step-by-Step construction, Manipulation, and animation
In the figure, a circle D is inscribed in the arbelos ABC (AB, BC and AC are semicircles), prove that KLFM is a square.



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gogeometry.com/geometry/archimedes_arbelo_circle_square_2.htm

Archimedes' Arbelos and Square

Dynamic Geometry Software. Step-by-Step construction, Manipulation, and animation
In the figure, a circle D is inscribed in the arbelos ABC (AB, BC and AC are semicircles), prove that ELBK is a square.



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gogeometry.com/geometry/archimedes_arbelo_circle_square.htm

Elearn Geometry Problem 211: 60 Degree Triangle, Areas

See complete Problem 211 at:
gogeometry.com/problem/p211_triangle_60_equilateral_area.htm

60 degrees triangle, equilateral triangle, areas. Level: High School, SAT Prep, College geometry

Archimedes' Book of Lemmas, Proposition #15

Problem 655: Inscribed Regular Pentagon, Arc, Midpoint, Perpendicular, Radius
Exercise your brain. Archimedes wrote the "Book of Lemmas" more than 2200 years ago. Solve the proposition #15 (high school level) and lift up your geometry skills.

Click the figure below to see the complete problem 655


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gogeometry.com/ArchBooLem15.htm

Archimedes' Book of Lemmas, Proposition #14

Problem 654: Salinon
Exercise your brain. Archimedes wrote the "Book of Lemmas" more than 2200 years ago. Solve the proposition #14 (high school level) and lift up your geometry skills.

Click the figure below to see the complete problem 654


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gogeometry.com/ArchBooLem14.htm

Archimedes' Book of Lemmas, Proposition #13

Problem 653: Diameter, chord, perpendicular
Exercise your brain. Archimedes wrote the "Book of Lemmas" more than 2200 years ago. Solve the proposition #13 (high school level) and lift up your geometry skills.

Click the figure below to see the complete problem 653.


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gogeometry.com/ArchBooLem13.htm

Archimedes' Book of Lemmas, Proposition #12

Problem 652: Diameter, chords, perpendicular, tangents
Exercise your brain. Archimedes wrote the "Book of Lemmas" more than 2200 years ago. Solve the proposition #12 (high school level) and lift up your geometry skills.

Click the figure below to see the complete problem 652


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gogeometry.com/ArchBooLem12.htm

Archimedes' Book of Lemmas, Proposition #11

Problem 651: Perpendicular chords and radius
Exercise your brain. Archimedes wrote the "Book of Lemmas" more than 2200 years ago. Solve the proposition #11 (high school level) and lift up your geometry skills.

Click the figure below to see the complete problem 651.


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gogeometry.com/ArchBooLem11.htm

Archimedes' Book of Lemmas, Proposition #10

Problem 649: Tangents, secant, chords, parallel, perpendicular
Exercise your brain. Archimedes wrote the "Book of Lemmas" more than 2200 years ago. Solve the proposition #10 (high school level) and lift up your geometry skills.



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gogeometry.com/ArchBooLem10.htm

Archimedes' Book of Lemmas, Proposition #9

Problem 648: Perpendicular chords and arcs
Exercise your brain. Archimedes wrote the "Book of Lemmas" more than 2200 years ago. Solve the proposition #9 (high school level) and lift up your geometry skills.



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gogeometry.com/ArchBooLem09.htm

Archimedes' Book of Lemmas, Proposition #8

Angle Trisection. Neusis Construction
Exercise your brain. Archimedes wrote the "Book of Lemmas" more than 2200 years ago. Solve the proposition #8 (high school level) and lift up your geometry skills.



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gogeometry.com/ArchBooLem08.htm

Archimedes' Book of Lemmas, Proposition #7

Problem 646: Square, inscribed and circumscribed circles
Exercise your brain. Archimedes wrote the "Book of Lemmas" more than 2200 years ago. Solve the proposition #7 (high school level) and lift up your geometry skills.



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gogeometry.com/ArchBooLem07.htm

Archimedes' Book of Lemmas, Proposition #6

Arbelos
Exercise your brain. Archimedes wrote the "Book of Lemmas" more than 2200 years ago. Solve the proposition #6 (high school level) and lift up your geometry skills.



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gogeometry.com/ArchBooLem06.htm

Archimedes' Book of Lemmas, Proposition #5

Problem 644: Arbelos, Archimedean Twins
Exercise your brain. Archimedes wrote the "Book of Lemmas" more than 2200 years ago. Solve the proposition #5 (high school level) and lift up your geometry skills.



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gogeometry.com/ArchBooLem05.htm

Archimedes' Book of Lemmas, Proposition #4, Arbelos

Problem 643
Exercise your brain. Archimedes wrote the "Book of Lemmas" more than 2200 years ago. Solve the proposition #4 (high school level) and lift up your geometry skills.



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gogeometry.com/ArchBooLem04.htm

Archimedes' Book of Lemmas, Proposition #3

Problem 642: Semicircle, Diameter, Perpendicular
Exercise your brain. Archimedes wrote the "Book of Lemmas" more than 2200 years ago. Solve the proposition #3 (high school level) and lift up your geometry skills.
Click the figure to view details.

Zoom

Archimedes' Book of Lemmas, Proposition #2

Problem 641: Diameter, tangents, perpendicular
Exercise your brain. Archimedes wrote the "Book of Lemmas" more than 2200 years ago. Solve the proposition #2 (high school level) and lift up your geometry skills.

Zoom

Archimedes' Book of Lemmas, Proposition #1

Tangent circles and parallel diameters (Problem 640)
Exercise your brain. Archimedes wrote the "Book of Lemmas" more than 2200 years ago. Solve the proposition #1 (high school level) and lift up your geometry skills.

Click the figure below to see the complete proposition.

Zoom

Archimedes' Book of Lemmas

Index.
According to "The Works of Archimedes" by T. L. Heath, Cambridge 1897, Archimedes' works included "On the Sphere and Cylinder", "On the Measurement of a Circle", "On Conoids and Spheroids", "On Spirals", "On the Equilibriums of Planes", "The Sand-reckoner", "Quadrature of the parabola", "On Floating Bodies", "Book of Lemmas" and "The Method".



In the book "Book of Lemmas", attributed by Thabit ibn-Qurra to Archimedes, there were 15 propositions on circles, with the first proposition referred in the subsequent fifth and sixth propositions. The statements in "Book of Lemmas" do not seem to concur to a central theme.

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Google Gadget: Archimedes' Book of Lemmas

Add "Archimedes' Book of Lemmas" to your iGoogle page.
iGoogle is a more personal way to use Google.com. Customize your page anyway you like, by adding your favorite themes and gadgets. Click the (+)Google button below.

Add "Archimedes' Book of Lemmas" to your iGoogle page.

Google Gadgets: GoGeometry

Add "GoGeometry" to your iGoogle page.
iGoogle is a more personal way to use Google.com. Customize your page anyway you like, by adding your favorite themes and gadgets. Click the (+)Google button below.

Add "GoGeometry" to your iGoogle page.

Google Gadgets: Golden Rectangles

Add "Golden Rectangles" to your iGoogle page.
iGoogle is a more personal way to use Google.com. Customize your page anyway you like, by adding your favorite themes and gadgets. Click the (+)Google button below.

Add "Golden Rectangles" to your iGoogle page.

Google Gadgets OpenSocial API

Mind Map
Gadgets powered by Google are miniature objects made by Google users like you that offer cool and dynamic content that can be placed on any page on the web.



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gogeometry.com/software/google_gadgets_opensocial_api_mind_map.html

Google Legacy Gadgets API

Mind Map
Gadgets powered by Google are miniature objects made by Google users like you that offer cool and dynamic content that can be placed on any page on the web.



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gogeometry.com/software/google_legacy_gadgets_api_mind_map.html

Geometry Quotes Quiz

Who said this? Five random questions.




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gogeometry.com/QuotesQuiz_1.htm

Nagel Point Puzzle

22 pieces of polygons
The lines connecting each vertex of a triangle ABC with the point of tangency between the opposite side and the opposite excircle are concurrent at a point called the Nagel point.



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gogeometry.com/puzzle/Puzzle_Nagel_point_center.htm

Gergonne Point Theorem. Concurrency.

Interactive proof with animation
The lines joining the vertices of a triangle ABC to the tangent points D, E, and F of the inscribed circle are concurrent at point G called the Gergonne point."



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gogeometry.com/gergonne.htm

Miquel Pentagram, Dynamic Geometry

Requires Java 1.3 or higher and Java enable browser
Take a pentagram ABCDE forming a convex pentagon FGHIJ and triangles AFJ, BGF, CHG, DIH, and EJI. Construct the circumcircles of triangles AFJ, BGF, CHG, DIH, and EJI. Then the five new points, K,L,M,N,P resulting from the intersection of two consecutive circumferences are concyclic (lie on the same circumference).



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gogeometry.com/javacar/Miquel_1.htm

Ceva's Theorem Puzzle

48 classic piece
A theorem relating the way three concurrent cevians (AD, BE, CF) of a triangle ABC divide the triangle's three sides.



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gogeometry.com/puzzle/Puzzle_Ceva_theorem.htm

Triangle with the bisectors of the exterior angles.

Collinearity
In any non-isosceles triangle ABC, the bisectors of the exterior angles at A, B, and C meet the opposite sides at points D, E, and F respectively. Prove that D, E, and F are collinear."



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gogeometry.com/triangleBisectExtCol.htm

Napoleon's Theorem

A purely geometric proof. It uses the Fermat point to prove Napoleon without transformations."



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gogeometry.com/Napoleon0.htm

Morley's Theorem Puzzle

Puzzle: 22 pieces of polygons.
Frank Morley was a member of Haverford College's Department of Mathematics in the early part of the twentieth century. He is credited with being the first to arrive at the celebrated Morley's trisector theorem:
"The three points of intersection of the adjacent angle trisectors of any triangle form an equilateral triangle."



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gogeometry.com/puzzle/Puzzle_Morley.htm

Morley's Theorem

Introduction with animation. Triangle + Trisectors = Equilateral triangle.
Frank Morley was a member of Haverford College's Department of Mathematics in the early part of the twentieth century. He is credited with being the first to arrive at the celebrated Morley's trisector theorem:
"The three points of intersection of the adjacent angle trisectors of any triangle form an equilateral triangle."



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gogeometry.com/geometry/morley_theorem_angle_trisector.html

Monge & d'Alembert Three Circles Theorem II

Dynamic Geometry
Given three disjoint circles A, B and C of unequal radii situated entirely in each other's exterior, the common internal tangents of circles A and C meet in Y, the common internal tangents of circles A and B meet in Z and the common external tangents of circles B and C meet in X. Then the points X, Y and Z are collinear.


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gogeometry.com/javacar/Monge_2.htm

Monge & d'Alembert Three Circles Theorem I

Dynamic Geometry
Given three disjoint circles A, B and C of unequal radii situated entirely in each other's exterior. Then the common external tangents taken in pairs, meet in three points X, Y and Z which lie on a line.


Continue reading at:
gogeometry.com/javacar/Monge_1.htm