(full name Hadji Muhiddin Piri Ibn Hadji Mehmed), was born on the European part of the Ottoman Empire) round 1460. When he was young, together with his uncle, a well-known corsair and seafarer of the time he took part in many naval wars of the Ottoman Empire .Later he started working on his studies about navigation.
By 1516, he was again at sea as a ship’s captain in the Ottoman fleet.In 1516 -17, he took part in the Ottoman conquest of Egypt. Piri had risen to the rank of Reis (Admiral) as the Commander of the Ottoman Fleet in the Indian Ocean and Admiral of the Fleet.
When the Portuguese turned their attention to the Persian Gulf, Piri Reis occupied the Qatarpeninsula and the island of Bahrain to deprive the Portuguese of suitable bases on the Arabian coast.
He returned to Egypt, when he was an approaching the age of 90. When he refused to support the Ottoman Vali (Governor) of Basra, Kubad Pasha, in another campaign against the Portuguese in the northern Persian Gulf, Piri Reis was beheaded in 1553.
Piri Reis is the author of the Kitab-ı Bahriye (Book of Navigation): one of the most famous pre-modern books, including a world map.
Although he was not an explorer, he made the first map to show parts of the Americas, the Piri Reis map, in 1513.
He drew a second map in 1528. Only a fragment of that map survives today. That fragment however, shows parts of North America, including Greenland. It goes from the coast of Labrador and Newfoundland in the north, to Florida,Cuba and parts of Central America in the south. Therefore, some people believe he drew a map of the Arctic about 200 years before it was discovered.
A century after Piri’s death and during the second half of the 17th century, a third version of his book was produced, which left the text of the second version unaffected while enriching the cartographical part of the manuscript. It included additional new large-scale maps. These maps were much more accurate and depict the Black Sea, which was not included in the original.
Copies of the Kitab-ı Bahriye are found in many libraries .
Rowan Gavin Paton Menzies
(born 14 August 1937) is a British author and retired submarine lieutenant-commander.
He is best known for his controversial book 1421: The Year China Discovered the World, in which he asserts that the fleets of Chinese Admiral Zheng visited the Americas prior to European explorer Christopher Columbus in 1492.
Fibonacci (c. 1170 – c. 1250)
Leonardo Fibonacci – an Italian mathematician, was considered by some “the most talented western mathematician of the Middle Ages.”
Recognizing that arithmetic with Hindu–Arabic numerals is simpler and more efficient than with Roman numerals, Fibonacci travelled throughout the Mediterranean world to study under the leading Arab mathematicians of the time. At the age of 32, he published what he had learned in Liber Abaci (Book of Abacus or Book of Calculation), and thereby popularized Hindu–Arabic numerals in Europe.
The book showed the practical importance of the new numeral system, using lattice multiplication and Egyptian fractions.
In the Fibonacci sequence of numbers, each number is the sum of the previous two numbers, starting with 0 and 1. This sequence begins 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987 … 
The higher up in the sequence, the more closely the ratio of two consecutive Fibonacci numbers will approach the golden ratio (approximately 1 : 1.618 or 0.618 : 1).
Paul Gallez (1920–2007)
was an Argentinian cartographer and historian, born in Brussels, and based on the city of Bahía Blanca, province of Buenos Aires, Argentina.
He made an extensive research on maps to show that America was known long before the Age of Discovery, inspired by previous works by Dick Edgar Ibarra Grasso and Enrique de Gandía.
He was the first to identify all the principal fluvial system of South America in the Henricus Martellus Germanus map of 1489, using a distortion grid.
He considers that fellow historians and himself constitutes the so called Argentine School of Protocartographyedit
Claudius Ptolemeuss; c. AD 90 – c. AD 168)
was a Greco-Roman citizen of Egypt who wrote in Greek. He was a mathematician, astronomer, geographer, astrologer, and of the greatest thinkers of his time. He lived in Egypt under Roman rule, but few reliable details of his life are known.Prolbably, he lived in Alexandria, where he died around AD 168.
Ptolemeus was the author of several scientific treatises, at least three of which were of continuing importance to later Islamic and European science. The first is the astronomical treatise now known as the Almagest (in Greek, Ἡ Μεγάλη Σύνταξις, “The Great Treatise”, originally Μαθηματικὴ Σύνταξις, “Mathematical Treatise”). The second is the Geography, which is a thorough discussion of the geographic knowledge of the Greco-Roman world. The third is the astrological treatise known sometimes in Greek as the Apotelesmatika (Ἀποτελεσματικά), more commonly in Greek as the Tetrabiblos (Τετράβιβλος “Four books”), and in Latin as the Quadripartitum (or four books) in which he attempted to adapt horoscopic astrology to the Aristotelian natural philosophy of his day.