Welcome to Geometry from the Land of the Incas

Geometry, Machu Picchu

Triangle and Squares Theorems

 

Geometry Step-by-Step from the Land of the Incas provides an eclectic mix of sound, science, and Incan history in order to raise students' interest in Euclidean geometry. Visitors will find geometry problems, proofs, quizzes, puzzles, quotations, visual displays, "scientific speculation", Cuzco, Machu Picchu, Lost City of the Incas, Nazca Lines, the Quipu, the Lord of Sipan, Caral: the oldest civilization in the Americas, and more. On July 7th, 2007, Machu Picchu was voted as one of New Open World Corporation's New Seven Wonders of the World. Site created and maintained by Antonio Gutierrez.


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Geometry from the Land of the Incas - Recent Additions (Page 1 of 14)

 

Classical theorems

 

Triangle, Angle Bisector, Circumcircle

Proposed Problem 400.
Triangle, Angle bisector, Circumcircle, Perpendicular, Congruence.

 

Inca exhibition in Brescia, Italy

Inca in Brescia: Live the Legend - Origin and Mysteries of the Golden Civilization”,.
Dec 4, 2009 - Jun 27, 2010.

 

Quechua: Inca tongue

Andean nations seek revival for ancient Inca tongue.
Argentina, Bolivia, Chile, Colombia, Ecuador, Peru.

 

RIght triangle, Midpoints, Distance

Proposed Problem 399.
Right triangle, Midpoints, Distance, Pythagorean theorem, Congruence.

 

Wassily Kandinsky, “Several Circles,” 1926

Several Circles (1926) by Wassily Kandinsky and the Golden Rectangle.

 

Parallelogram, Area

Proposed Problem 398.
Parallelogram, Area, Similarity, Congruence.

 

Yma Sumac Index

Yma Sumac Index,
'Peruvian songbird', 'Nightingale of the Andes', 'The Castafiori Inca'
Inca Music: noted Peruvian soprano.

 

 

Triangle, Altitude

Proposed Problem 397.
Triangle, Altitude, Midpoints, Congruence.

 

The Lost Symbol, Dan Brown

The Lost Symbol by Dan Brown, Word Cloud. Mind map of characters, Interactive Washington D.C. map, Videos.

 

Square, Angle trisectors

Proposed Problem 396.
Square, Angle Trisectors, Congruence, Area.

 

Related Geometry topics

Related Geometry Topics:
Computational, Manifold, Topology, String theory, Coordinate, Analytical, Trigonometry, Projective, Algebraic, Differential, Symplectic, Lie theory, Fractal, Dimension theory, Computer graphics, Atiyah, Gromov, Perelman.

 

Square, 15 degree

Proposed Problem 395.
Square, 15 Degree, Equilateral triangle.

 

Geometry Jobs

Related Geometry Jobs Topics: Design, Construction, Architecture, Interior design, Furniture, Engineer, Physicist, Astronomer, Plumbing, Cabling, Lighting, Acoustic, Roads, Maps, Navigational system, GPS, CAD, Gardening, Computer games, Robotics, Computational geometry, Medical imaging, Structural engineering, Protein modeling, Surveyor, Finite element analysis, Stock market, Programmer, Java, Teacher, Landscaper, Set Design, Graphic designer, Digital animator, Art

 

Cerro Verde Copper Mine

Maps and News: Cerro Verde Mine.
Explore Cerro Verde, Arequipa, Tacna, Peru through detailed satellite imagery.

 

Kosnita theorem

Kosnita's Theorem.
Circumcenters, Concurrent lines.

 

Pierina Gold Mine

Maps and News: Pierina Mine.
Explore Pierina Mine, Ancash, Peru through detailed satellite imagery.

 

Square, Circle

Proposed Problem 394.
Square, 90 Degree Arc, Diagonal, Congruence.

 

Yanacocha Gold Mine

Maps and News: Yanacocha Mine.
Explore
the geometry of Yanacocha, Cajamarca, Cuzco, Peru through detailed Google satellite imagery.

 

Antamina Mine

Maps and News: Antamina Mine.
Explore the geometry of Antamina, San Marcos, Huari, Ancash, Peru through detailed satellite imagery.

 

SAT: how important is geometry

How Important is Geometry on the SAT?
Video.

 

Toquepala Mine

Maps and News: Toquepala Mine.
Explore Toquepala, Ilabaya, Tacna, Peru through detailed satellite imagery.

 

Caterpillar, Open Pit Mining Operation

Caterpillar 797F, Open Pit Mining Operation. Video.

 

Triangle, Orthocenter

Proposed Problem 393.
Triangle, Orthocenter, Circumcircles, Congruence, Collinear.

 

Bingham Canyon Mine

Bingham Canyon Mine. Video
World's Largest Mine - Bingham Canyon Open Pit Copper Mine.

 

Triangle, Parallel, Concurrent lines

Proposed Problem 392.
Triangle, Parallel lines, Concurrent lines.

 

Bingham Canyon Mine, Super open pit

Maps and News: Bingham Canyon Mine.
Explore the geometry of the Bingham Canyon Mine, Utah through detailed Google satellite imagery.

 

Triangle, Parallel, Collinear points

Proposed Problem 391.
Triangle, Parallel lines, Collinear points.

 

Super pit gold mine

Maps and News: Fimiston Super Pit gold mine.
Explore the geometry of the Super Pit gold mine, Western Australia through detailed Google satellite imagery.

 

The Fimiston Super Pit gold mine

The Fimiston Super Pit gold mine. Video.
Australia's largest open cut gold mine.

 

Median of a triangle, Index

Median Index.
Theorems and Problems.

 

Killke Pottery

Pre-Inca Killke Pottery, Mind Map
Killke and Killke-Related Pottery from Cuzco, Peru, in the Field Museum of Natural History by Brian S. Bauer and Charles Stanish.

 

 

Inti Raymi, Cuzco

The Inti Raymi
Video.

 

 

Triangle, Parallel, Collinear points

Proposed Problem 390.
Triangle, Parallel lines, Collinear points.

 

Khalil Gibran (1883 – 1931)

Video: Khalil Gibran, a Restrospective

 

Triangle, Parallel, Harmonic Mean

Proposed Problem 389.
Triangle, Parallel lines, Harmonic Mean.

 

Brandon Jennings

Brandon Jennings Mind Map.
Jennings' 55 Points Sets NBA Record. November 14, 2009.

 

Triangle, Angle bisector, Perpendicular, Parallel

Proposed Problem 388.
Triangle, Angle bisector, Perpendicular, Parallel.

 

Triangle, Angle Bisector, Perpendicular, Concyclic points

Proposed Problem 387.
Triangle, Angle bisector, Perpendicular, Concyclic points.

 

Kseniya Simonova - Sand Animation - Ukraine's Got Talent 2009 Winner

Kseniya Simonova - Sand Animation.
2009 Winner of Ukraine's Got Talent Video
.

 

Triangle, Angle bisectors

Proposed Problem 386.
Triangle, Angle bisector, Perpendicular, Parallel, Semiperimeter, Congruence.

 

Khalil or Kahlil Gibran Index

Kahlil Gibran Index.

 

Triangle, Angle bisectors

Proposed Problem 385.
Triangle, Angle bisector, Perpendicular, Parallel, Semiperimeter.

 

Triangle, Angle bisectors

Proposed Problem 384.
Triangle, Angle bisector, Perpendicular, Parallel, Semiperimeter.

 

Khalil or Kahlil Gibran 16 mm Film

Khalil Gibran: 16 mm Film
Video.

 

Philosophy of Mind

Philosophy of Mind, Interactive Mind Map.

 

Concave Quadrilateral, Angle bisectors

Proposed Problem 383.
Concave Quadrilateral, Angle Bisectors, Semi-difference of Angles.

 

Chord Index

Chord. Index.
A chord of a circle is the line segment joining two points on the circle. 

 

US Capitol Rotunda

The United States Capitol rotunda.

 

Mathematics Selections

Mathematics Selections.

 

Euclidean Geometry Selections

Euclidean Geometry Selections
Random articles.

 

Geometry, random articles

Geometry - Math Selections
Random articles

 

Algebraic Geometry

Algebraic Geometry Selections

 

Projective Geometry

Projective Geometry Selections

 

Western Art

Western Artists: 500 Years of Women in Art.

 

Surfing: Geometry of tube shape

Surfing: Geometry of tube shape.

 

Western Artists

Western Artists: 500 Years of Male Self Portraits.

 

Eugene Delacroix

Eugene Delacroix (1798 -1863).

 

Library of Essential Reading Mind Map

Library of Essential Reading.
Mind Map.

 

Van GOgh "Self Portraits"

Vincent van Gogh:"Self Portraits".
Video.

 

 Bali, Jimbaran

Jimbaran, Bali, Acintya.

 

Pigeons Rock, Beirut

Pigeons Rock, Raouche, Beirut.

 

Pigeons Rock, Beirut

Pigeons Rock, Raouche, Beirut.

 

Pigeons Rock, Beirut

Pigeons Rock, Raouche, Beirut.

 

The Quipu, Inca Empire Index

The Quipus, Index.
The Quipus and The Royal Commentaries of the Inca, 1609, Caral: Ancient Peru city reveals 5,000-year-old 'writing', The Quipus and Hiram Bingham, The Quipucamayocs, The Quipu Video

 

 

Quipu Illustrations by Guaman Poma

The Quipus: Illustrations from 1615 by Felipe Guaman Poma de Ayala

 

 

Royal Commentaries of the Incas

The Royal Commentaries of the Incas.
by Inca Garcilaso de la Vega.
Mind Maps: Book I, Book II, Book III, Book IV, Book V, Book VI, Book VII, Book VIII, Book IX

 

Royal Commentaries, Word Cloud

The Royal Commentaries of the Incas.
Word Cloud, Common terms and phrases.

 

Quadrilateral, Angle Bisectors

Proposed Problem 382.
Concave Quadrilateral, Angle Bisectors, Angles.

 

Quadrilateral, Angle Bisectors

Proposed Problem 381.
Quadrilateral, Diagonals, Angle Bisectors, Angles.

 

Pre Inca Ceramics

Pre-Inca, Ceramics of Ancient Peru.
Mind Map.

 

Triangle, Excenter, Parallel

Proposed Problem 380.
Triangle, Excenter, Parallel to a side, Angle, Congruence.

 

Triangle, Excenter, Parallel

Proposed Problem 379.
Triangle, Excenter, Parallel to a side, Angle, Congruence.

 

The Incas Mind Map

The Incas Mind Map.
Based on 'The Incas' by Terence N. D'Altroy.

 

Triangle, Incenter, Parallel to a side

Proposed Problem 378.
Triangle, Incenter, Parallel to a side, Angle, Congruence.

 

Triangle, Altitude, Angle bisector

Proposed Problem 377.
Triangle, Internal Angle Bisector, Altitude.

 

Triangle, Excenter, Internal and External angle bisector,

Proposed Problem 376.
Triangle, Excenter, Internal and External Angle Bisectors.

 

Triangle, Excenter, Angle

Proposed Problem 375.
Triangle, Excenter, External Angle Bisectors.

 

Tiangle, Incenter, Angle

Proposed Problem 374.
Triangle, Incenter, Internal Angle Bisectors.

 

Inca Gold Mining

Inca Gold, Mining.
Index.

 

Problem about square and inscribed circle

Proposed Problem 373.
Square, Inscribed Circle, Diagonal, Perpendicular, Angle.

 

Circles, Common tangent

Proposed Problem 372.
Circles, Common Internal and External Tangent, Angles.

 

Square, Triangle, Area, Circle

Proposed Problem 371.
Square, Inscribed circle, Triangle, Area.

 

SAT Math Practice Index

SAT Math Practice,
Index.

 

SAT MAth Problem 1

SAT Math Practice 1,
Video.

 

Inca Gold Nazca-Ocona

The Tesoro Gold Project, Peru, St. Elias Mines.
The Property covers approximately 2000 hectares (5000 acres) and is part of the well-known gold-bearing Nazca-Ocona belt that is located in southern Peru.

 

Stanford Engineering video course

Programming Methodology Course, Stanford University / Engineering, Video Lectures
open educational resource lectures by Professor Mehran Sahami for the Stanford Computer Science Department (CS106A).

 

Chan Chan: 17 Wood Statuettes

Peruvian archaeologists find 17 500-year-old wood statuettes.
Trujillo, Peru.

 

Triangle with squares, Circumcircles

Proposed Problem 370.
Triangle with squares, Circumcircles, Tangent circles.

 

Intersecting circles, chord, angle, congruence 

Proposed Problem 369.
Intersecting circles, Chord, Center, Angle, Congruence.

 

Triangle, 120 degrees, angle bisectors

Proposed Problem 368.
Triangle, 120 degrees, Angle bisectors, Perpendicular.

 

Square, 45 degrees

Proposed Problem 367.
Square, Angle, 45 degrees, Pythagoras, Congruence, Similarity.

 

Equilateral triangle, circumcircle

Proposed Problem 366.
Scalene triangle, Circumcircle, Angles, 60 Degrees, Equilateral triangle.

 

English ESL Second Language

English ESL Index
English as a Second Language (ESL)

 

Circular sector 60 degrees

Proposed Problem 365.
Circular Sector of 60 degrees, Midpoints, Perpendicular, Congruence.

 

The Lost Symbol, Dan Brown

The Lost Symbol by Dan Brown, Word Cloud.

 

Triangle area, Circle, Curvilinear triangle

Proposed Problem 364.
Obtuse triangle, Congruence, Circles, Diameter, Curvilinear triangle, Area.

 

Proto-Quechua Mind Map

Proto-Quechua Mind Map.

 

Quechua Language Index

Quechua Index

 

Right triangle, Congruence, Angles

Proposed Problem 363.
Right triangle, Congruence, Angles.

 

Obtuse Triangle Index

Obtuse Triangle.

 

Macheroni Constructions Index

Mascheroni construction with compass alone. Index

 

Special Right Triangle 30-60 Index

Special Right Triangle 30-60.

 

Special right triangle 30 60

Special Right Triangles.

 

The Road Not Taken by Robert Frost, Word Cloud

Word Cloud of "The Road Not Taken"

 

Top Electric Guitar Players

The 10 Best Electric-Guitar Players.

 

Circle, Chord, Perpendicular

Proposed Problem 362.
Circle, Chord, Perpendicular, Equal chords.

 

Cloud Computing

Cloud Computing Word Cloud
Weighted list in visual design

 

Euclid's Elements Book I

Euclid's Elements Book I Word Cloud.

 

Word Cloud Index

Word Cloud or Tag Cloud Index
Weighted list in visual design

 

Trigonometry Word Cloud

Trigonometry Word Cloud.

 

Metro Systems Index

Metro Systems Index.

 

ISO Standards Index

ISO Standards Index.

 

Abacus in Japan

The Abacus in Japan: Amazing Math Video.

 

Right triangle, Incircle, Angle

Proposed Problem 361.
Right triangle, Incircle, Incenter, Tangency points, Angle.

 

ISO-9000 Word Cloud

ISO 9000 Word Cloud.

 

Word Tag Software

Word Cloud Software Generator.

 

Master Degrees Word Cloud

Master Degrees Word Cloud.

 

Area of Triangle, Circles, Diameters

Proposed Problem 360.
Area of a triangle, Curvilinear triangles, Circles, Diameters.

 

Toronto Sheppard Line (TTC)

Toronto: Sheppard Line TTC and Golden Rectangles.
The Sheppard Line is the newest subway line in Toronto, Ontario, Canada, operated by the Toronto Transit Commission.

 

COBIT: Control Objectives for Information Technology

COBIT: Control Objectives for Information and related Technology.
Interactive Mind Map.

 

Cyclic quadrilateral, Rhombus

Proposed Problem 359.
Cyclic quadrilateral, Angle bisector, Rhombus.

 

Chartres Cathedral window

North Rose Window at Chartres Cathedral. Golden Rectangles.

 

Isosceles triangle 80 80 20

Proposed Problem 358.
Isosceles triangle 80-80-20, Circle, Angles, Congruence.

 

Atlanta Marta

Atlanta MARTA: Metropolitan Atlanta Rapid Transit Authority and Golden Rectangles.
MARTA is the principal rapid-transit system in the Atlanta metropolitan area and the ninth-largest in the United States.

 

St Matthias Church

Rose Window at Church of St Matthias, Richmond. Golden Rectangles.

 

Mascheroni Construction with compass alone

Mascheroni construction: Find the center of a circle with compass alone.

 

Square, Exterior point, Triangle, Area

Proposed Problem 357.
Square, Exterior point, Triangles, Area.

 

Square, Triangle, Area

Proposed Problem 356.
Square, Point inside, Triangles, Area.

 

Amazon, ASME Best Cover2009

Amazon.com: Best Magazine Covers of the Year. Call for Entries
Customers Who Vote for This Year's Best Magazine Cover Automatically Get a Chance to Win a $10,000 Amazon.com Gift Card.

 

Algebra Index

Algebra Index.
Interactive Mind Map
Algebra History
Algebra Classification
Elementary Algebra

 

Mac OS X Reference Library mindmap

Mac OS X Reference Library, Interactive Mind Map.
Based on Developer.apple.com: Mac OS X Reference Library

 

Strasbourg Cathedral window

Rose window at Strasbourg Cathedral. Golden Rectangles.

 

Circles, Tangent, Concyclic points

Proposed Problem 355.
Circles, Common external tangent, Concyclic points.

 

Machu Picchu window 5

Machu Picchu Window 6.

 

Rhombus, Square 

Proposed Problem 354.
Rhombus, Square, 45 degrees.

 

Machu Picchu window 4

Machu Picchu Window 4.

 

Tangential quadrilateral, Incircle, Inradius

Proposed Problem 353.
Tangential quadrilateral, Diagonals, Incircles, Inradii.

 

Machu Picchu window 3

Machu Picchu Window 3.

 

Tangential quadrilateral

Proposed Problem 352.
Tangential quadrilateral, Incircles, Common tangent, Circumscribable or Tangential quadrilateral.

 

Rhombus, Circumscribable quadrilateral

Proposed Problem 351.
Rhombus, Incircles, Common tangent, Circumscribable or Tangential quadrilateral.

 

Computer Knowledge Centers

Computerworld Knowledge Centers.
Interactive Mind Map

 

Fields of Mathematics Mind map

Fields of Mathematics, Interactive Mind Map.
Mathematics can be subdivided into the study of quantity, structure, space, and change.

 

Triangle, Cevian, Incircles, Angles

Proposed Problem 350.
Triangle, Cevian, Incircles, Tangents, Tangency Point, Angles.


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