**A Controversy For The Days Of Last Decline**

*Archeologists Deal Final Blow To Geometry*

**Times Science Report**

Lupold Wendershaft, Ph.d, F.A.A.A.S, D.D.

Geometry, which was long considered the most elegant and irrefutable of the sciences, was dealt the last of a series of deadly blows last week with the unveiling of a five year archeological dig.

“The age of Euclid is over” said Wermer Heisenstat, referring to the famous geometrical theorist whose work was once required reading for every elementary school pupil, “While his model has been very much under fire for most of the last few years, we have finally found the definitive evidence in the fossil record.”

Theorists have long called into question the progression of Euclid’s most well known text *Elements,* though it was not until recently that scientists began to call into question the trigonocentric- that is, triangle based- nature of Euclid’s various proofs, a critique that was originally put forth in Erhard Schroeder’s now famous work *The Two Missing Sides of Euclid’s Triangle. *

*“*Euclid essentially treats the triangle as distinct from other shapes” explains Harvard’s John Benson, “In Euclid, there is a bright line distinguishing the triangle from the pentagon, for example. This naturally lead to a kind of divinization of the triangle, which explains why it was featured as such a prominent part of medieval cathedrals. In light of the new evidence, however, we can see that older distinction as a somewhat naive mistake, one that we can now definitively correct using the fossil record.”

scholars have long disputed the natural basis of geometry, but until now the debate lacked the sort of hard evidence that could silence a dwindling body of theorists that held to the natural priority of the triangle model in geometric theorems. The debate centered around Euclid’s foundational belief that the triangle was the basis for the generation of the pentagon. “Euclid treats the pentagon as essentially an afterthought to the triangle” Benson explains, “If anyone looks for the pentagon in the *Elements* he or she will have to go through half the book before Euclid even mentions it. The new evidence suggests that Euclid is progressing in exactly the wrong way, since pentagonal shapes are found 35 million years before triangular shapes in the fossil record.”

The release of the evidence was met with a firestorm of controversy. Harvey Longman, a senior research fellow at the Aleithia Institute, took issue with the dating of the fossils: “there is simply no way to accurately parse the strata of late chronolithic sediments” he said, and then quickly added “the evidence is pretty convincing, I must admit, but we can’t forget the teaching value of Euclid, who still provides a pretty good model for the distinction of shapes, even if it is ultimately not entirely in line with natural history.”

In spite of the tremendous success of the newer pentagonal theorems among the archeologists, there was a note of reflection and regret. “We have all gotten used to assigning a certain priority to the triangle, and we have grown to see it as a sort of separate, distinct, and wholly autonomous shape” said Schroeder. “But we can no longer accept the sort of exalted position that the triangle has. It is, in the end, only a sort of warped pentagon, a shape which proceeded out of a random selective process progressing over 30 to 40 million years.”

“There is a part of us that is sad to see Euclid go” said Schroeder “But that is simply the way science is. Upheavals are what makes the study of any science so satisfying to participate in.”

——–