Geometry Problems, Online Education

Machu Picchu: The Enchanting Incan Citadel Overlooking the Urubamba Valley

Illustration: Machu Picchu: The Enchanting Incan Citadel
Machu Picchu's Golden Rectangles Embrace: A View Framed by Mathematical Harmony.

 "Machu Picchu is a late Inca town dramatically sited on the saddle between two mountains, Machu Picchu (Old Mountain) and Huayna Picchu (Young Mountain), overlooking the Urubamba River, which winds 3000 ft below it. Its buildings, all constructed of local stone, use various types of walling, from coursed ashlar to roughly dressed rubble, and incorporate characteristic trapezoidal doorways. Some of the walls have rectangular niches formed on the inner side. Masonry gables still stand and some buildings have trapezoidal window openings. The steep slopes of the site are terraced with masonry retaining walls to hold soil for the gardens, and the various levels of the town are linked by stone stairways."
Sir Banister Fletcher. A History of Architecture. p688.

Machu Picchu is a pre-Columbian Inca city located at 7,970 ft altitude on a mountain ridge above the Urubamba Valley in Peru, about 44 mi northwest of Cusco. Machu Picchu is the most familiar symbol of the Inca Empire. It is often referred to as "The Lost City of the Incas". The site was designated as a World Heritage Site in 1983 when it was described as "an absolute masterpiece of architecture and a unique testimony to the Inca civilization".

Machu Picchu, which means "Old Peak", was probably built by Pachacuti Inca as a royal estate and religious retreat in 1460-70. The site is comprised of approximately 200 buildings, most being residences, although there are temples, storage structures and other public buildings. It has polygonal masonry, characteristic of the late Inca period.

After centuries lost in the jungle of Cuzco, Machu Picchu was rediscovered in 1911 by the American archaeologist Hiram Bingham. The Inca trail to Machu Picchu is rated as one of the best trekking trails in the world offering stunning landscapes and ancient ruins with diverse ecology.




The Inca used trapezoids for all their windows and doors,
which withstand earthquakes well.



Door of the Amarus



Machu Picchu and Huayna Picchu photography

"Then up the ladder of the earth I climbed
through the barbed jungle's thickets
until I reached you Machu Picchu.

Tall city of stepped stone,
home at long last of whatever earth
had never hidden in her sleeping clothes.
In you two lineages that had run parallel
met where the cradle both of man and light
rocked in a wind of thorns."

Pablo Neruda 1904-1973
Chilean Poet (Nobel 1971)


Factories and Industrial Sector


The Intihuatana, or "hitching post for the sun," is a granite block carved into the peak of the mountain where Machu Picchu lies, high in the jungle-covered Andes


The Intihuatana was used by Inca astronomers to predict solstices and was of great importance in Inca mythology and agriculture. It is considered the most important shrine in Machu Picchu.