### The Rubáiyát – Omar Khayyám

This is a page from a manuscript of the *Algebra* (*Maqalah fi al-jabra wa-al muqabalah*) of Omar Khayyam (1048-1131). This work is known for its solution of the various cases of the cubic equation by finding the intersections of appropriately chosen conic sections. On this page, Omar is discussing the case “a cube, sides and numbers are equal to squares”, or, in modern notation, x^{3} + cx + d = bx^{2}. The two conics whose intersection provides the solution are a circle and a hyperbola. In the case illustrated, these curves intersect twice, thus providing two (positive) solutions of the given cubic equation. Khayyam even provides a problem which leads to this case: Divide ten into two parts so that the sum of the squares of the parts together with the quotient of the division of the greater by the smaller be seventy-two. For more details, see pp. 90ff of Daoud Kasir, *The Algebra of Omar Khayyam* (New York: Teachers College Press, 1931) or pp. 144ff of R. Rashed and B. Vahabzadeh, *Omar Khayyam, the Mathematician* (New York: Bibliotheca Persica Press, 2000).

This particular manuscript was copied in the thirteenth century in Lahore, India. Among the other fourteen works contained in the volume are two by Sharaf al-Din al-Tusi (1135-1213) on determining vertical heights of objects and a treatise by ibn al-Haytham (965-1039) on the astrolabe.

### Robert Schock – Solar Outburst – Goebekli Tepe – Forgotten Civilization

My comments below were written shortly after my first visit to Göbekli Tepe in 2010. I have been back many times since, studied the scholarly literature, and spoken with the late Dr. Klaus Schmidt on site regarding the dating of the remains and other matters. I plan to update and revise this page when time permits. In the meantime, please enjoy what is posted below and, if you would like more, my book *Forgotten Civilization: The Role of Solar Outbursts in Our Past and Future* offers a great deal (including a color photo insert that contains images of Göbekli Tepe). Another article on this website, “Rising from the Ashes of SIDA”, also discusses various aspects of Göbekli Tepe.

Robert Schoch and **John Anthony West** at Göbekli Tepe in 2010

**The 12,000-year-old Megalithic Complex that is Rewriting History**

In May 2010 I traveled to Turkey with my wife, Catherine Ulissey, and my friend and colleague John Anthony West. It was an incredible trip, and here I will note only a few highlights.

First we flew to Istanbul, where we spent the day visiting the area of the hippodrome, the Blue Mosque, and the Hagia Sophia. Our time there was all too short, as we had to catch our flight to Antep (Gaziantep), and from there we drove to Urfa. Our primary destination was to visit Göbekli Tepe.

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