The Cicada (pronounced Sah-kay-dah) are winged insects that evolved over 1 million years ago when North America was experiencing retreating glaciers. They spend most of their life underground feeding on the juice of plant roots. They emerge from the ground, mate and die very quickly. But they embody startling behavior in that this process of life, mating and death is synchronized in periods of years that are prime numbers. A prime number is an integer such as 11, 13, 17; a number that has no positive divisors other than 1 & itself.
Cicada's begin digging exit tunnels in their 13 & 17 years. Dr. Mario Markus of the Max Planck Institute for Molecular Physiology located in Dortmund, Germany discovered evolutionary models of interactions between predator and prey such as the cicada.
At the end of summer many places echo with the sound of the male cicadas loud mating calls. The name cicada means “tree cricket” and their songs are made from a special organ called a tymbal near their trachea.
The song of the cicada is embodied in Mariachi music in Latin American festivals and weddings. In the famous La Cigarra, the cicada is represented as an insect that sings until its death.
In Aesop’s Fables, the story The Cicada and the Ant the cicada represents a carefree singing insect enjoying life of song and leisure while the industrious ant is preparing for winter.
Dr. Markus' published work is available here for review: http://www.mariomarkus.com/hp9.html
Sounds of Cicada's http://www.cicadamania.com/audio/
The Rhind Papyrus provides the best evidence for the history of early math among ancient Egyptians.
It is a scroll about a foot high and 18 feet long. It was discovered in a tomb in the city Thebes.
The source of the scroll is a man named Ahmes. Writing began in Egypt around 1650 B.C., the Rhind Papyrus is dated at 1680 B.C. It provides evidence involving fractions, addition, arithmetic progressions, building and accounting. We can deduce the beginnings of algebra, pyramid geometry and practical mathematics for surveying.
It is currently at the British Museum after being purchased by Alexander henry Rhind (1833-1863) a Scottish historian visiting the Luxor market in 1858.
BRITISH MUSEUM- RHIND MATHEMATICAL PAPYRUS
WIKIPEDIA- THE RHIND MATHEMATICAL PAPYRUS
The origin of zero begins in the Indian northern sub-continent, where a stone tablet called the Bakhshali Stone (pronounced bock-shall-ee) was discovered in the town of Gwalior, just outside of Delhi, India. This is the first documented archeological find providing researchers with evidence to trace the origins of zero.
However, other cultures give us clues.
The ancient Babylonians didn't have a symbol for zero, this caused both uncertainty and political anxiety for political dynasties that wish permanent subjugation of their people. The library of Nineveh (Mosul, Iraq) shows great care temple priests acting as accountants devoted to maintenance of official archives. Babylonian scribes left an empty space for zero in their digits, providing consternation for discerning beginning or ending of numerical citations. Eventually, the Babylonians did enforce the use of symbolic notation for zero, however, this did not resolve the cognitive difficulties associated with the absence of zero.
Although the Mayan Empires of Central American highlands did have zero, their remoteness prevented any cultural ascendancy in commerce, astronomy or in the emergence of social, political institutions to consolidate this discovery.
The emergence of Muslim Eurasian nomads immediately after the ascendancy of the Mongol Empire provides great evidentiary support tracing the movement of the concept of zero moving west from the eastern Mediterranean originating in the Indian sub-continent.
With the introduction of zero from Islamic nomads, we have an astonishing achievement in conformity for modeling any achievement in astronomy, accounting or commerce.
Historical bibliography: Bakhshali Manuscript and the Ganita Sara Samgraha (850 A.D., other notable Indian mathematicians were Brahmagupta (d. 668 A.D. pronounced Brah-mag-goo-pa, Bhaskara (d. 680 A.D. pronounced Bass-car-rah, and finally Mahavira d. 870 A.D. pronounced Mah-haa-vira).
The most notable Islamists is Al-Samawal's The Dazzling (1150 A.D.), and finally into the eastern Mediterranean landing in Byzantine Florence with Fibonacci's 'Liber Abaci' (1202 A.D.)
A significant discovery has shook the mathematical world: Prime numbers are not actually random. Apart from two and five, every single prime number finishes with either one, three, seven, or nine. If there was no arrangement, then the chance of having two consecutive primes ending with either number should constantly be 25 percent, but that's not always the case. Kannan Soundararajan and Robert Lemke Oliver of Stanford University in California have revealed that in the first 100 million prime numbers, a prime ending in one is followed by another ending in one 18.5 percent of the time, by three 29.7 percent, by seven 30 percent, and by nine 21.8 percent. In other words, the prime's final number is most likely not to be repeated.