THALES OF MILETUS
CALCULATING THE HEIGHT OF CHEOPS PYRAMID

Thales of Miletus
• Around the 620 BC • Miletus was an ancient Greek city on the western coast of Anatolia in what is now Turkey • Philosopher, astronomer, geographer, mathematician… • Great observer and traveller.

• In one of his travels to Egypt he aimed to measure the height of the Great Pyramid of Cheops. • There are many theories about how he accomplished his goal but there is agreement that he used the concept of similarity of triangles.

Similar triangles
Triangles are similar if they have the same shape, but not necessarily the same size. Have all the same angles. Its correspondent sides are proportional.

PROPORTION?

PQ QR PR P 'Q ' Q ' R ' P ' R '

17 15 12 2 8,5 7,5 6

PROPERTY
Two right angled triangles are similar when one of their angles other than the rigth ones (90º) are equal in measure. Isoceles right angled triangles

The sun is so far away that we might consider its rays parallel and so, they hit the tops of all the objects at the same slant.

h = Thales’ height H = Height of the pyramid

H h h Pyramid S (shade)
s (shade)=h

What was really new?
• • Do you see what Thales did? He used an abstract right triangle! He pictured the height of the Great Pyramid as an imaginary post from its top straight down to its base. Such an imaginary post would cast an imaginary shadow, all the way from where it stood at the center of the pyramid to the tip of the pyramid's real shadow: so the length of this imaginary shadow would be the length of the base plus the actual projecting shadow!

...Sketch: Thales and Hypatia
Thales
While it is clear that Euclid definitely set a precedent for geometry and mathematics as a whole, he was not alone in his work, his endeavors, or his ideas. He certainly was not the first to come up with these theories or rules for geometry either. Before there was Euclid, there was Thales of Miletus. Thales, along with other mathematicians or “geometers” laid some of the foundation for...

...Thales of Miletus (ca 624 - 546 BC) Greek domain
Thales was the Chief of the Seven Sages of ancient Greece, and has been called the "Father of Science," the "Founder of Abstract Geometry," and the "First Philosopher." Thales is believed to have studied mathematics under Egyptians, who in turn were aware of much older mathematics from Mesopotamia. Thales may have invented the notion of compass-and-straightedge...

...Benjamin Foster
9-15-2011
Philosophy 101-501
"Thales"
In Brian Magee's " Story of Philosophy" he composed that Thales,the pre Socratic
Greek philospher of Miletus and founder of Milesian school,taught that everything in nature
is composed of one basic matter.Thales presumed that water the was the fundamental
building block of all things and the Earth floated on water.In Joseph Carter's lecture he states
that "Thales...

...Thales (624 BC-546 BC) lived in Ancient Greece and was arguably the world's first philosopher and scientist.
Prior to Thales, supernaturalism was considered to be the cause of most if not all things. For example, the answer to a question such as, "Why does the wind blow?" or "What caused the epidemic?" would invariably involve a supernatural explanation such as, "It is the will of the gods."
Explanations based on supernaturalism, however, are not really...

...Thales’ Theorem
Thales’ Theorem simply states that if three points exist within a circle, and one of those points is the diameter of the circle, then the resulting triangle will always be a right triangle. This simple idea can become very useful for certain applications such as, identifying the center of a circle with its converse. On the triangle the vertex of the right angle always terminates at the ends of the diameter line. By locating the two points of...

...point in shaping the culture of future generations. It resulted in many wars and conquests but ultimately this mistake is why today delegates to the United Nations wear suits and ties instead of turbans.
Aristagoras was the Persian governor of Miletus on the edge of the Persian Empire. The nearby island of Naxos rebelled against the Persian Empire and Aristagoras seized the opportunity to take it back and get a promotion to a better position from the Persian emperor...

...Although the Greek culture didn't believe in Animism, an Ionian named Thales
adopted this idea in his own way. Thales was born in the Greek city-state of Ionia in the
mid 620's(BC.) Thales did not only study knowledge philosophy, but also practiced
science, history, engineering, geography, and politics. Thales was the first of his time to
propose theories of a primary substance that causes change, and supports the universe....

...Although the Greek culture didn't believe in Animism, an Ionian named Thales
adopted this idea in his own way. Thales was born in the Greek city-state of Ionia in the
mid 620's(BC.) Thales did not only study knowledge philosophy, but also practiced
science, history, engineering, geography, and politics. Thales was the first of his time to
propose theories of a primary substance that causes change, and supports the universe....

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