Line Triangle

Line Triangle

Suppose that a Simson line of a triangle is perpendicular to one of the sides of the triangle. Show that the?

pole must be one of the vertices of the triangle.
Note: Simson's Theorem: Let P be any point on the circumcircle of triangle ABC and let X, Y, and Z be the feet of the perpendiculars dropped from P to line BC, AC, and AB, respectively. Then points X, Y, and Z are collinear.

If the presumed Simson line is perpendicular to one side and the pole is not at the opposite vertex, then the other two Simson points do not lie on the presumed Simson line and the presumption is false Thus the pole must be at the opposite vertex. I believe there is also an analytical proof showing that the Simson line approaches the perpendicular to the side as the pole approaches the opposite vertex.

Flying Over The Nazca Lines

‘The Lines and Geoglyphs of Nasca and Pampas de Jumana' became a United Nations Educational, Scientific and Cultural Organization (UNESCO) World Heritage site in 1994 on the grounds that they are "among archaeology's greatest enigmas because of the quantity nature, size and continuity."  Located in the Peruvian coastal plains about 250 miles south of Peru's capital city of Lima the lines are easily accessible to tourist who are traveling down the coast by bus on the Pan American highway or by air.  It is highly recommended to take at least a day on your Peru vacation or South American adventure to see these mysterious lines thought to have been created between 500 B.C. and A.D. 500.

Although you do not have to take an airplane to see them, the bird's eye view is much better than the constructed viewing platforms.   Not only will you be able to see more of the lines themselves, you will also be able to get a better view and awesome pictures from one of the many airplanes that fly overhead.

Said to have had ritual astronomical functions, these figures depict living creatures such as the hummingbird, monkey and spider, stylized plants and geometric shapes such as the triangles, trapezoids, spiral, shell and tree, and of course the famous astronaut in which many conspiracy theories have developed.  Although the more than 70 lines resemble Paracas motifs, it is commonly said that these lines were created by the Pre-Inca Nasca culture. 

So what exactly are the lines?  The lines are shallow lined designs on the ground made by removing the reddish iron-oxidized pebbles that cover the dry earth in this part of Peru to uncover the whitish ground beneath providing a sharp contrast in color from far above.  Being one of the driest deserts on earth with very little wind, the lines have been well preserved.     

The most commonly accepted theory of these lines is that the Nazca culture created these lines to be seen by their deities based on their understanding of astronomy and cosmology and their desire to pray to the gods for water.  There are also many alternative theories, one of which is that the Nazca culture had access to and used hot air balloons. One Swiss author states that the Nazca culture was far more technologically advanced than we consider and they were used as ancient airfields.  Both are not substantiated due to lack of archaeological evidence. Some still believe that they are anamorphic diagrams of the constellations found in the sky but there is little evidence to back this up too.  Other largely disregarded theories involve alien activity on earth, saying that extraterrestrials came to earth to create these lines. 

Whatever the theory, there are many environmental concerns about the preservation of the lines.  The vibrations of the Pan American highway have been of great concern as well as the seismic activity along the Pacific coastline.  Pollution and erosion due to deforestation in the region are also both large concerns.  These combined could lead to the erasing of the lines in the relatively near future and attempts at preservation are still being used.  Be sure that this is part of your trip to ensure you don't miss out on this unique and mystery filled area and of course to cast your vote on how you think these lines were created!  

 

About the Author

This guide to Nasca during Peru vacations was written by a Peru travel expert at Peru For Less, specialists in high value, fully customizable tours and packages.

Line Triangle

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