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Inca Trail to Machu Picchu, the Lost City of the Incas

 

Geometry problems | Inca Geometry | Quizzes | Puzzles | Quotes | Inspiration |  Triangle centers | Landscape of terms | News | MindMap

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 Geometry Theorems & Problems  

 Inca Geometry

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Apollonius' Tangency Problem for Three Circles Illustration with animation and sound.

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Archimedes' Book of Lemmas:Try to solve the Archimedes' problems of geometry (High school Level)

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The Archimedes Palimpsest

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Archimedes: 3.14159 is Close Enough

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Archimedes Index

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Blanchet Theorem

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Brahmagupta's Theorem Cyclic quadrilateral.

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Butterfly Theorem Proof. Puzzle.

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Butterfly Theorem Introduction.

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Carnot's Theorem

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Ceva's Theorem Concurrency

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Circles

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Clifford's Circle Chain Theorems

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Einstein and Pythagoras theorem proof

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Equilic Quadrilateral Five theorems.

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Equal Incircles Theorem. Interactive presentation.

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Eyeball Theorem

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Fagnano's Problem

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Feuerbach Theorem

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Feuerbach Point, Acute Triangle illustration

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Geometry, table of contents

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Gergonne Point Theorem

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De Gua's Theorem

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Johnson Theorem

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Heron's Formula. Key facts and a purely geometric step-by-step proof

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Kurschak's Tile and Theorem

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Langley Theorem. Adventitious angles.

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Lemoine Theorem

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Lunes of Hippocrates 1, 2 , 3, 4

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Mascheroni Construction with compass alone. Midpoint of a segment.

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Menelaus' Theorem. Triangle and transversal line.

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Miquel's Pentagram Theorem Proof

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Miquel's Pentagram Dynamic Geometry

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Monge & d'Alembert Three Circles Theorem I Dynamic Geometry

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Monge & d'Alembert Three Circles Theorem II Dynamic Geometry

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Morley's Theorem

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Nagel Point Theorem Proof

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Napoleon's Theorem

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Newton's Theorem

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Nine-Point Center, Nine-Point Circle, Euler Line

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Parallelogram&Squares

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Pascal's Mystic Hexagram Theorem Proof

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Pentagons and Pentagrams. Menelaus and Collinearity.

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Platonic Solids Interactive animation

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Poncelet's Theorem

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Proposed Problems about congruence of line segments, angles, and triangles.
Key Theorems or Facts to know

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Proposed Problem 29, Geometry Help: Facts you should know

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Proposed Problem 39.

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Proposed Problem 39 Geometry Help.

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Ptolemy's Theorem.

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Pythagoras Right Triangles, Formulas and Facts

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Pythagoras and Circle Area

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Cyclic Quadrilateral: Ratio of the Diagonals 

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Quadrilaterals Table of Content

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Sangaku Problem 1

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Sangaku Problem 2

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Sangaku Problem 3

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Sangaku Problem 41. "Mickey Mouse."

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Sawayama -Thebault's theorem

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Semiperimeter and Incircle

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Semiperimeter and Excircles

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Semiperimeter, Incircle and Excircles

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Seven Circles Theorem

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Simson Line

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Simson Line: Angle

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Steiner's Theorem

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100° Isosceles

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Triangles

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Triangles and Lissajous Art

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Triangle with the bisectors of the exterior angles. Collinearity.

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Triangle and Squares. 19 theorems, visual illustrations.

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Triangle and Squares 18 Sangaku Problem

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Triangle and Squares 19

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Triangle&Squares 0 Two squares

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Triangle&Squares 1 Two squares

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Triangle&Squares 2 Two squares

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Triangle&Squares 3 Three squares

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Triangle with Squares 4 Finsler-Hadwiger Theorem

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Triangle with Squares 5: Median and Altitude

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Triangle with Squares 6: Four squares

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Triangle Centers

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Van Aubel's Theorem

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Adjacent Angles

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Varignon & Wittenbauer

 

 Triangle Centers

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Centroid

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Orthocenter

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Circumcenter

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Incenter

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Excenter

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Apollonius Point

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Nine-Point Center, Nine-Point Circle, Euler Line

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Gergonne Point See also: Gergonne Point Theorem Proof

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Nagel Point See also Nagel Point Theorem Proof

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Fermat Point

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Napoleon Point

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Bevan Point The circumcenter of the excentral triangle. Illustration with animation.

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Symmedian (Lemoine) Point

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Mittenpunkt Point

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Steiner Point

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Bevan Point Puzzle

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First Ajima-Malfatti Point

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Second Ajima-Malfatti Point

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Spieker Center

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Triangle Centers Word Find Puzzle

 

 Inspiration for Problem Solving

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Archimedes & Rhombicuboctahedron  Archimedes "The Geometer"

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Experiencing Geometry Poem

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Top Ten Reasons to Enjoy Geometry

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Euler and his beautiful and extraordinary formula

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The Landscape of Geometry Terms

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Machu Picchu and Geometric Art

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Paracas Cultures Fabrics

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The Lord of Sipan and Geometric Art

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Angkor Wat and Geometric Art

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Giza Pyramids and Geometric Art

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Vatican City and Geometric Art

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Morley's Theorem

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Hyperbolic Tessellation and Geometric Art.

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Hexagon and Lissajous Art  

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Pentagon and Lissajous Art  

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Triangles and Lissajous Art

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Simson Line

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Sierpinski Triangle and Machu Picchu with fractals.

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Nazca Lines Animation. Mystery on the Desert.

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Nazca Lines: The Monkey. Geometric Art.

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Home Introduction

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Geometric Art. Table of Content

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The School of Athens. Interactive Map.

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The School of Athens. Perspective: the Central Vanishing Point.

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Fermat's Last Theorem

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Geometry in Action: Branching into geometry. Espaliered fruit trees can take many forms

 

 

 The election of the New Seven Wonders of the World

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Ranking of the New 7 Wonders finalists as of Jan 31, 2007

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Acropolis, Athens, Greece

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Alhambra, Granada, Spain

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Angkor, Cambodia

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Chichen Itza, Yucatan, Mexico

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Christ Redeemer, Rio de Janeiro, Brazil

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Colosseum, Rome

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Easter Island Statues

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Eiffel Tower, Paris, France

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Great Wall, China

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Kiyomizu Temple, Kyoto, Japan

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Machu Picchu, Peru

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Statue of Liberty, New York, USA

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Sydney Opera House

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Taj Mahal, Agra, India

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Timbuktu, Mali

 

 
 

 Home

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 Home - Welcome

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Recent additions

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Recent additions (continuation)

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Home - Introduction

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Random Entry Randomly sends you to one of the web pages of this web site.

 
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Cuzco Ancient Inca Empire Capital.

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Inca History according to Guaman Poma's work in 1615.

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Inca Calendar

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The Thirteen Towers of Chankillo, Peru.
Stone Towers Are Decoded as Earliest Solar Observatory in the Americas.

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Cuzco City Map

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Cuzco Panorama View

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Cuzco Sacsayhuaman Fortress. Panorama View.

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Cuzco Chinchero Panorama View

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Machu Picchu Lost City of the Incas.

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Machu Picchu and Geometric Art

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Machu Picchu and the Flower of Life

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Machu Picchu Map Interactive with zoom.

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Machu Picchu and Sierpinski Triangle.

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Machu Picchu Condor's Eye View

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Machu Picchu and the Bridge

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Machu Picchu and the 21 finalist for the New Seven Wonders of the World

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Machu Picchu, interactive panorama view from San Miguel Mountain.

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Machu Picchu Trekking View.

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Machu Picchu: Top Ten Feats of Man-Made Wonder, Picked by Structural Engineers

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Inca Trail to Machu Picchu Panorama View

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Inca Trail to Machu Picchu

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Inca Trail to Machu Picchu: Huinay Hayna

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Lake Titicaca and the Inca Manco Capac

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Inca Quipu Data Structure.

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Nazca Lines One of humanity's mysteries.

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Nazca Lines Animation. Mystery on the Desert.

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Nazca Lines: The Monkey. Geometric Art.

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Nazca Lines, the Hummingbird. Satellite image and size comparison.

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Nazca Lines: "The Needle and Thread"

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Nazca Lines: The Condor bird. Puzzle: 40 pieces of birds tessellation.

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Nazca Lines: The Spider, Puzzle: 44 pieces in a tri-dove style of piece.

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Choquequirao, an ancient Inca site

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The Lord of Sipan King Tutankhamen of the Americas

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Pre-Inca Sican treasures of Peru's Pomac Forest

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The Lord of Sipan and Geometric Art

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The Lord of Sipan and Spiderman Gold Necklace

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Looted Peru Moche Headdress Recovered in London

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Caral: the oldest civilization in the New World  Peru opens Caral ruins to tourists.

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Vicunas, Inca Gold of the Incas

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The Incas and their Civilization

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The Incas and Architecture

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The Incas and Civil Engineering

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The Incas and Irrigation

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The Incas and Domestic Animals.

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The Incas Language: Quechua.

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The Incas and Pottery

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The Incas and Metallurgy.

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The Incas and Weaving.

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The Incas and the People.

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Inca City on Mars? South Polar Region on Mars. NASA Mariner 9.

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Faces on Mars and Earth

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Colca Canyon and Pre-Inca Terraces

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Chachapoyas Mummies.

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Chachapoya Pre-Inca ruin discovered in Peru. January 17, 2007

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About Peru Lima, Cuzco, Machu Picchu, Nazca Lines, Titicaca Lake, Biosphere reserves, Amazon River, Paracas, and more.

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UNESCO World Heritage Sites in Peru

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Paracas Cultures Fabrics

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Geometry and Cultures

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Inca Music

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Peruvian Music: Grupo Nectar Tragedy  

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Sierpinski Triangle and Machu Picchu fractal illustration with animation

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Sierpinski Triangle and Machu Picchu Puzzle.

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The Stone of twelve angles Puzzle: 22 pieces of polygons.

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Machu Picchu Puzzle: 41 pieces of polyominoes.

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The Lord of Sipan Puzzle: 22 pieces of polygons.

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The Lord of Sipan: Spiderman Puzzle: 50 pieces of circles.

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Inca Quiz. Ten questions in random order.

 

 Quizzes

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Inca Quiz. Ten questions in random order.

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Geometry Quotes Quiz. Five questions in random order.

 

 Puzzles

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Play Sudoku Online, Rules and Tips

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The Stone of twelve angles Puzzle: 22 pieces of polygons.

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Cuzco City

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Machu Picchu Puzzle: 41 pieces of polyominoes.

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Bevan Point Puzzle.

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Butterfly Theorem Puzzle.

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Ceva's Theorem Puzzle.

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Equal Incircle Theorem

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Euler's Formula Puzzle: 55 pieces of six star.

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Golf and Geometry

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Inca Music

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Morley's Theorem - Puzzle 22 pieces of polygons.

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Nazca Lines: The Condor bird. Puzzle: 40 pieces of birds tessellation.

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Nazca Lines: The Monkey Puzzle

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Nazca Lines: The Spider, Puzzle: 44 pieces in a tri-dove style of piece.

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Nagel Point Puzzle: 22 pieces of polygons.

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Newton's Theorem Puzzle: 50 pieces of circles.

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Pentagons & Pentagrams: 96 pieces of triangles.

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The Oldest  Quipu

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Sierpinski Triangle and Machu Picchu Puzzle.

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The Lord of Sipan Puzzle: 22 pieces of polygons.

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The Lord of Sipan: Spiderman Puzzle: 50 pieces of circles.

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The Raft of the Medusa. Puzzle: 91 pieces of a lizards tessellation.

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The Raft of the Medusa (Traditional Chinese version). Puzzle: 91 pieces of a lizards tessellation.

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The Raft of the Medusa (Spanish version). Puzzle: 91 pieces of a lizards tessellation.

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The Road Not Taken Robert Frost's poem. Puzzle 48 pieces of USA map.

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Sangaku Problem

 

 Quotes

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Archimedes: diagram

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Aristotle: Limit

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Banach: mathematician

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Cocteau: freedom

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Coxeter: exploring

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Crelle: triangle

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Descartes: reasoning

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Dürer: art

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Euclid: royal road

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Fermat: Last theorem

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Fontenelle: elegant

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Freud: visualizing

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Galileo: The Universe

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Hobbes: Pythagoras

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Ibn Khaldun: Intellect

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Kepler: God

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Lafayette: Liberty

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Lagrange: Algebra

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Leonardo: proof

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Lincoln: Euclid

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Mandelbrot: fractals

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Newton: principles

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Pappus: bees

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Pedersen: skill

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Pythagoras: music

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Plato: eternal

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Plutarch: Archimedes

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Poincaré: natural selection

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Polya: elegance

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Pushkin: inspiration

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Regiomontanus: triangle

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Riemann: proofs

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Thales of Miletus

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Valéry: similar figures

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Voltaire: no sects

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Wittgenstein: contradict

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Shortest Distance

 

  World News

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Existence of a geometric module in the brain?

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NC State University paleontologist: 5-foot penguins populated prehistoric Peru

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Baseball and Math: Yankees Will Dominate Baseball This Year

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The Geometry of Musical Chords

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Pre-Inca Sican treasures of Peru's Pomac Forest . Pre-Inca burial site found.

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Fermat's Last Theorem

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Tissue Geometry Plays Crucial Role in Breast Cell Invasion

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Engineer leaves career to teach geometry

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Navier-Stokes Equation, Millennium Prize $1 million

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Robert Frost Poem Discovered

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Geometry in Action: Artery Geometry

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Looted Peru Moche Headdress Recovered in London

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Poincare Conjecture: Russian to turn down million dollar prize for maths.

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Geometry Of Blood Vessels May Influence Heart Disease

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Duke Engineers Probing Contortions of the Heart's Blood Vessels

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Tattooed mummy puzzles scientists in Peru.

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Celestial Find at Ancient Andes

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Japanese Find New Nazca Lines In Peru.

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Machu Picchu and Yale University.

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Peru: from the art of the Chavin to the Incas. 3,000 years of Peruvian art on show in Paris.

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Humans Hard-wired for Geometry

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Baby Got Math

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Recent additions

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Awards

 

  MindMaps

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    Van Hiele Model of Geometric Thought

 

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Last updated: September 8, 2007