SOME MARINE SLUGS

By Andreea Nicoleta Radu

NEMBROTHA KUBARYANA

The Nembrotha Kubaryana is a species of colourful sea slug in the family of Polyceridae.

It can reach the 12 cm of length and it's dark-bodied with green stripes running down the body or have green raised spots. Its foot and head are in the middle of a red-orange and the rinophores can be red or green.

These animals live in the Indo-West Pacific and they are feeding ascidans an, above all, on green-ringed ascidan.

Nembrotha kubaryana uses the toxins in its prey ascidians to defend itself against predators. It stores the ascidian's toxins in its tissues and then releases them in a slimy defensive mucus when alarmed.

CHROMODORIS LOCHI

Chromodoris Lochi is a marine gastropod mollusk in the family of Chromorididae.

This animal is blue and sometimes blueish.white with three dark lines across its body. It can reach 34 mm in length and the gills and the rinophores are a translucent straw-color, trought to pink and light orange.

Chromodoris Lochi, like other slugs, feeds on sponges.

This species of slug is found in the tropical Western Pacific Ocean and is known from the Great Barrier Reef in the Southern Hemisphere to the Philippines in the Nothern Hemisphere.

NEMBROTHA PURPUREOLINEATA

The Nembrotha Purpureolineata is a dorid nudibranch in the family of Polyceridae.

This species is a large pale-bodied dorid. Its ground colour is a creamy white and it's mostly hidden by a large brown patch which covers most of its body. Usually it has brown stripes running down the sides of the body and round the head. The rinophores are red to orange-red and its foot is purple. It may reach a toal length of 120mm.

This slug feed on ascidians and tunicates, most of them on the yellow-lined ascidian Clavelina Meridionalis.

It's located in the west of the tropical Indo-West Pacific Ocean.

HYPSELODORIS BENNETTI

Hypselodoris Bennetti is a colourful sea slug and a marine gastropod mollusk in the family ofChromodorididae. It has a turquoise-blue body and a bright yellow mantle edge. There are red spots on its under body. The gills and the rinophores are white, outlined with pink or red. It can reach a total length of 50 mm and it feeds on sponges from the genus Psammocinia.

This nudibranch is found in Southearsten Australia from Queensland to Victoria.

PHYLLODESMIUM POINDIMIEI

This species of sea slug is an olid nudibranch in the family of Facelinidae.

It can reach a length beetwen 12-50 mm. Its body is composed by long pink spots.

This species contains zooxanthellae. It feeds on the octocoral Carioja Riisei. The crab Thalima Integra is a predator of Phyllodesmium poindimiei.

We can found this marine slug in Australia, New Caledonia and Hawaii.

MEXICHROMIS MULTITUBERCULATA

Mexichromis Multitberculata is a species of sea slug and a dorid nudibranch in the familyChromorodididae.

This slug can reach a total length of 30 mm. It has purple spots around the edge of the mantle. The mantle also has purple tipped tubercules.

It is found in a lot places:

• Indonesia

• Malaysia

• Papua New Guinea

• Sulawuesi

• Egypt

• Thailand

• Seto

• Kii

• Japan

• Hainan Island

• Hong Kong

  
  

Pythagoras

By Juan Tutasi

Pythagoras of Samos was an Ionian Greek philosopher, mathematician, and founder of the religious movement called Pythagoreanism. 
Most of the information about Pythagoras was written down centuries after he lived, so very little reliable information is known about him. He was born on the island of Samos, and might have travelled in his youth, visiting Egypt and other places looking for knowledge.
Pythagoras made influential contributions to philosophy and religious teaching in the late 6th century BC. He is often named as a great mathematician, mystic and scientist, but he is best known for the Pythagorean theorem which carries his name.
Many of the accomplishments credited to Pythagoras may actually have been accomplishments of pythagorichs.
It was said that he was the first man to call himself a philosopher, or lover of mathemathics, and Pythagorean ideas exercised a marked influence on Plato, and through him, all of Western philosophy. Many mathematical and scientific discoveries were atributed to Pythagoras, including his famous theorem, as well as discoveries in the field of music, astronomy, and medicine.But it was the religious element which made the profoundest impression upon his contemporaries. 
His followers established a select brotherhood or club for doing mathematics. All that was done there, the members kept it in secret. The death and his age of death is unknow, but we know that he is buried in a cave of Samos.



Pythagorean theorem

Since the fourth century AC, Pythagoras has been given credit for discovering the Pythagorean theorem, a theorem in geometry that states that in a rectangle triangle the square of the hypotenuse is equal to the sum of the squares of the other two sides—that is,

a^2 + b^2 = c^2

. This theorem is very important because, with it you can do many calculations.

                                                                              

The History of the Mathematics

By Juan Tutasi
 
Prehistoric mathematics (35,000 BC. -20,000 BC.)


The History of the Mathematics is so extensive that we'll begin since 35,000b.c-20,000b.c when were found the firsts mathematical ''texts'', which were bones and pieces of rocks that seems someone had written straight lines on. But why did the human been feel the necessity of using the mathematics? The origin of mathematical thought begins with the concepts of number, magnitude and form. In the Prehistoric age, the mathematics were so useful -not as nowadays-, for example, in Egypt it was necessary to know when  the river passed across the village to improve agriculture, or to know how many animals they have. Later the first civilisations (5,000b.c) incorporated some geometric pictures like the square, circle and the rectangle.



The oldest known possible mathematical object is the Lebombo bone, discovered in the Lebombo mountains of Swaziland and dated to approximately 35,000 BC. The first known mathematics were the Indians (3000bc-2000bc), they used the mathematics for the construction and they invented the decimal system.
It consists of 29 distinct notches cut into a baboon's fibula.
All of the above is disputed however, the currently oldest undisputed mathematical utilisations are from Babylonian and dynastic Egyptian sources.

First civilisations (3000 BC. -2600 BC.)

When the humans, with knowledge of math
ematics,  began building houses, and living all together with more people. The first civilisations where in Egypt and India. The Egipcians used the mathematics for building their famous pyramids, sculptures, and for knowing when the Nilo was going to overflaw their crops. The Egipcians created the first number system and a metric system, this was the first discovery and it has been developing until the modern geometry. In India the mathematicians created the decimal system which we use nowadays, this discovery allows us to make mathematic operations that are useful for technology and other sciences. The first Indian's civilisation created the number 0 that reduces many calculations, but it was unknown in Europe until the Roma Empire decadence.


Ancient Orient (1800 BC. -500 BC.)

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In Mesopotamia, nowadays  Irak, the mathematics were very useful. The ancient sumeries created the Mesopotamia's civilisation. In their discoveries we can find the multiplication table and they began to write their discoveries in clay rocks, because this rocks were very soft and you can write on with a stick. But they didn't use the same number simbology we use, they had a special mark for each number. This rocks were used in the trades for knowing how much they earned during a week, or for not to forget if someone had to pay you money that he hadn't paid you yet. This mathematics weren't written in decimal system, because they used to write in sixtieh system, it was more difficult but they didn't know about the decimal system. During this period the Indian mathematics didn't improve a lot because Indians used them for cultivation , the spirituality, and meeting the souls. Nevertheless the mathematics in Egipt improved during the helenistic period, they combined the mathematics with other sciences and they found the relation between mathematics and this other sciences. The babilons had a very short number, they only had six number : 1 ;10 ,100 ; 1,000 ; 100,000 and 1,000,000. The faraons in Egypt order the mathematicians to build the pyramids, because these were used as tombs, they also used them for some religious purposes.

Ancient Indian (900BC. -200 AC.)

The oldest mathematic documents from India are the Sulba Sutras, these are religious texts with

simple rules for constructing altars of various shapes, such as squares, rectangles, parallelograms and others. As Egypt, the Indians were veryworried with religion. In Sutras Sulba, there are methods for constructing circles with approximately the same area as a square, which approaches to the number π. Additionally, the Indians obtained the value of the square root of 2 with a lot of approximation, that belows to the lists of Pythagorean triples and the statement of the theorem of Pythagoras. All these results are present in Babylonian mathematics, indicating the strong influence of Mesopotamia. It is unclear, however, how far the Sutras Sulba influenced Indian mathematics. But there is a lack of continuity of the mathematics in India; and there were long periods of inactivity.

Ancient Greece (600BC. - 300 AC.)

Greek mathematicians lived in cities scattered the Eastern Mediterranean, from Italy to North Africa,
but they had a common language and a common culture. Greek mathematics of the period following Alexander the Great are called Hellenistic mathematics.
Greek mathematics were more sophisticated than the mathematics that had been developed before and only the most intelligent people of that period could learn and teach mathematics. It is believed that greek mathematics began with Thalesand Pythagoras. These mathematics, were probably inspired by Egyptian mathematics, Mesopotamian and Indian. According to legend, Pythagoras traveled to Egypt to learn mathematics, geometry and astronomy from Egyptian priests.
Tales used geometry to solve problems as calculating the height of pyramids and the distance of ships from the coast. Pythagoras is credited with the first theorem, the Pythagorean Theorem. Pythagoras created a school and his members who were called Pythagoreans  proved the existence of irrational numbers. Other famous mathematicians were Euclid who gave the earliest example of the mathematical methodology used today. He studied conics and wrote the book Elements, also did Archimedes of Syracuse who used the method of calculating the area under the arc of a parabola with the help of the sum of an infinite series, and gave an approximation of pi.

Roman Empire decadence (300 AC. 450 AC.)

Romans had already conquered Europe since 27 BC. and put their orders and laws. It is during the period of decadence, when the war and power became more important than culture. It was difficult to acquire knowledge, there weren't famous mathematicians from this period, because to the numerical system which was very bad for the calculation, women could not study and the men had to go to war. After the decadence of the Roman Empire, people began to use another number system, and everyone could study mathematics and others sciences.

Classical China and Japan(500 BC. - 1300 AC.)

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In China, the Emperor Qin Shi Huang gave the order that all books of the state have to be burned. The order was not obeyed by all the world, but as a result we know very little about mathematics in ancient China. The oldest math book that survived from the burning was the I Ching, trigrams and hexagrams using philosophics, mathematicians and mystics. These mathematical theorems are composed of lines called yin (female) and yang (masculine). After the burning of books, the Han Dynasty produced works mathematics that were burnt. In summary, the mathematical works of Han astronomer and inventor Zhang Heng contained a formulation for pi very approximate. Zhang Heng used his formula to find espheric volumes. Chinese also made ​​use complex combinatorial diagram known as magic square and magic circle. The Chinese and European mathematics remained separated, until the exchange between the two cultures between the sixteenth and XVIII.
The Japanese mathematics of this period was inspired by Chinese mathematics are essentially oriented to geometric problems. They solved "geometric puzzles' on wood tables called sangaku where they wrote some theorems like the Soddy theorem.

Classical India (400 AC. - 1600 AC.)

The advances in Indian mathematics after Sutras are the Siddhantas Sulba, that are astronomical theory and which shows strong Hellenistic influence. The Surya-Siddhanta introduced the trigonometric functions of sine, cosine and inverse sine and established rules to determine the trajectories of the stars in the positions in the sky. This work was translated from Arabic into Latin in the Middle Ages. In the V century, Aryabhata type Aryabhatiya, a muslim volume designed to complement the rules of calculation where was used in astronomy and mathematical measure, but certain things, which were later corrected, were wrong. For the first time Sphuta Brahma-siddhanta, explained clearly the uses of the number 0. Arab Students exported this knowledge to Europe by the twelfth century and ended up using the previous numbering systems of the world, the roman numbers. From the fourteenth century, Madhava, founder of the Kerala School, computed the value of the number π to 3.14159265359... . Progress in mathematics and other sciences in India were stopped after the Muslim conquest of Europe and India.

Medieval Islam (800 AC. -1500 AC.)

The Islamic Empire established across the Middle East, Central Asia, North Africa, Iberia, and part of India, made ​​significant contributions to mathematics. But not all of the texts were written in arabic, some were written in latin and greek. There weren't only arabian mathematicians, many other important Islamic mathematicians were Persians. In the ninth century, Al-Khwarizmi wrote several important books about Arabic numerals and methods of solving equations. The word algorithm is derived from the Latin of his name, Algoritmi, and the word algebra from the title of one of his works, Al-Kitāb fī al-Mukhtasar al-Gabr Hisab wa'l-Muqabala. Al-Khwarizmi is often nickname "the father of algebra", for their important contributions to this field. The further development of algebra came from the hand of Al-Karaji. In his theorem al-Fakhri extends the methodology to include infinits and unknown quantities. During this period, many important mathematic theories were discovered . When the Muslims were expelled from Europe, the advancement of mathematics increased more after their expultion.

Mathematics in the West (Europe) (1500 AC - 1800 AC)

Medieval Age

During the Middle Ages, people began to use algebra in trade, irrational numbers were used in some more sciences, a habit that was transmitted through all Europe. Also negative solutions were accepted to certain problems and imaginary quantities.
The development of mathematics during the Middle Ages is motivated by the belief in a "natural order" of arithmetic, geometry, astronomy and music, and Greek and Arabic mathematical works were improved.

 

European Renaissance

During the twelfth century, especially in Italy and Spain, were translated Arabic texts and some Greek texts were rediscovered. Toledo became a cultural center of translation; European students traveled to Spain and Sicily in search of scientific literature including the arabian texts. The economic and commercial growth that Europe experienced improved use of mathematics in people who were'nt mathematicians.
The new sources gave a boost to mathematics. Fibonacci wrote his Liber Abaci were he talks about the number Fi or golden number . Thomas Bradwardine invented some theories of the dynamic movement. The mathematicians of this period had to use approximate results because they didn't know the calculus also know as infinitesimal calculus. Until the late sixteenth century, the mathematicians had a problem with their solution because mathematicians searched exact answers of some problems but didn' t know how.

The Scientific Revolution of the XVIIth and XVIIIth

During these centuries, the mathematicians prefered physical and technical aspects. Isaac Newton and Gottfried Leibniz created calculus, which opens the era of Mathematical Analysis, the derivative, integration and differential equations and solve the problem that mathematicians through all the history had . The mathematical universe of this period was dominated by the figure of Leonhard Euler and his contributions on mathematical functions and numbers theories. The mathematical function became an object of study with his own subjects at universities.
In arithmetic, Euler proved Fermat's little theorem, which was difficult problem of this age, and gave an extended version of the composite numbers.

XIXth Century (1800 AC. -1900 AC.)

This is one of the most important periods of maths, because most of mathematics we use today were discovered during these years.
The nineteenth century mathematical history is very rich and extense. Numerous theories appeared new and some earlier works were complete. The number of professionals increased a lot and mathematics took a big importance ever before. The applications of mathematics in other sciences were developing, making believe that whithout mathematics science can't do anything, for example, the discovery of a new planet only by calculation, or the explanation of the creation of the solar system with maths. The domain of physics, experimental sciences, were completely invaded by mathematics: heat, electricity, magnetism, fluid mechanics, strength of materials and elasticity, chemical kinetics, were all ''mathematichzed''. The most important mathematicians of this period were: Joseph-Louis Lagrange, Augustin Louis Cauchy, Carl Friedrich Gauss also called the Prince of the Math, Bernhard Riemann, Pierre Laplace, William Rowan Hamilton and Gottlob Frege.

XXth Century (1900 AC. - 2000 AC.)

During the twentieth century mathematics became one of the greatest professions.
Each year, thousands of doctors graduated, and the job opportunities were in teaching and industry. Many new disciplines developed with the work of Poincaré like: topology, differential geometry, logic, algebraic geometry, Grothendieck's work.In a speech in 1900 in the International Congress of Mathematicians, David Hilbert proposed a list of 23 mathematical problems. This list, touched several areas of mathematics, it was a central focus for many mathematicians of the twentieth century. Until now, 10 have been resolved,7 partially resolved and 2 are still open and 4 aren't complete enough for knowing if they are resolved or not. Many conjectures were finally proved . The invention and continued progress of computers, and electronic machines allowed to work  faster with large amounts of information, . The speed information of computers also allowed to solve problems that would consume too much time on calculations using paper and pencil.

XXI Century (2000 AC- ....)

In 2000, the Clay Mathematics Institute announced the seven millennium problems, and in 2003 the demonstration of the Poincaré conjecture was solved by Grigori Perelman (who declined the prize). The prize for solving one of these problems is a Fields Medal (the Oscar of mathematics) and $ 1,000,000.

Most mathematical excercices and theorems have online version and printed, also leave many digital publications, so everyone can learn maths by their own. But this is not the end of way of mathematics, there are still many things to discover ....