Recent Changes

Wednesday, March 5

  1. file tessellations.jpg (deleted) uploaded Deleted File
    1:32 pm

Thursday, July 28

  1. page Escher edited ... {Escher_1.jpg} FIGURE 3 Escher often used animals and weird creatures in his tessellations, a…
    ...
    {Escher_1.jpg} FIGURE 3
    Escher often used animals and weird creatures in his tessellations, and in other paintings too, like in FIGURE 4 and FIGURE 5.
    ...
    FIGURE 4 {tessellations.jpg} FIGURE 5
    We don't really know why he used animals so much, or why he loved them, but it is clear that he did. He said, "While I was sitting so quietly alone, a very small bird hopped over the snow-perhaps it was a wren. It was enjoying the weather; it blinked merrily at the sun. It skipped toward the water and fluttered about a bit. Then it flew away, so I left too." This shows that he appreciated nature and took all of it in to include it in his art.
    Many of Escher's works are shown as optical illusions. Some are in museums, and some are in kids' play places, like a Florida science hands-on museum, Wonder Works. Though Escher liked optical illusions, they were not the starting point of his work. (M.C. Escher Legacy: A Centennial Celebration. P. 7) FIGURE 6 shows a simple panting by Escher. It looks as though one box is longer than the other, but if measured, they are exactly the same. FIGURE 2 could also be considered an optical illusion.
    (view changes)
    5:06 pm

Saturday, June 5

  1. page Diophantus edited ... Diophantus's first work was with polygonal numbers, on which he wrote a short essay about in t…
    ...
    Diophantus's first work was with polygonal numbers, on which he wrote a short essay about in the Arithmetica. He explained this through a method where numbers are represented by line segments. In his books Diophantus illustrateds how to solve linear equations, (this would be the beginning of them). In the same readings, Diophantus also showed how to solve quadratic equations. The 130 thirty problems that were in the Arithmetica mainly included equations that were determinate and indeterminate. Since no one was very familiar with his work at the time, they didn't understand well and it was very complex to most people.
    A determinate equation is an equation that has defined limits, or that is established, definite. It is an equation that has a definite answer that is not infinite and only has one possible solution. An example of this would be: 5-3=2. The example problem in determinate because it only has one solution, which is 2. The equation 5-3=2 cannot be derived any other way because it is determinate and only has one single solution. This is not only for this problem, but all determinate equations.
    ...
    would be: a xax + by=c.
    These were the first forms of algebraic expressions, and he also included integers. These infinite solution equations were also able to be simplified down to one answer. Since Diophantus was the first to deal with the indeterminate equations he was lucky enough to have them named after him. They are currently known as the Diophantine Equations. Diophantus was also the first mathematician to actually treat a fraction as a number. These new thoughts and thinking processes gave a whole twist on math and what it was going to be.
    Diophantus wrote other books from the Arithmetica collection. One in particular was called, "The Porisms". This book also disappeared with the other books in the Arithmetica. Some people have an impression that this could have been one of the lost books in the Arithmetica. The book, "The Porisms" was generally written about rational numbers and how they are to be used. There is another book that was authored by Diophantus, and that was, "Preliminaries to the Geometric Elements". This book was originally thought to be written by the Hero of Alexandria, another mathematician in Diophantus's time. Then, researchers show that the credit was falsely given to Hero and it really belonged to Diophantus.
    (view changes)
    4:51 pm

Monday, March 1

  1. page Pythagoras edited Type QPythagoras By Lewis Frame A very important figure in the content math world to this day…
    TypeQPythagoras By Lewis Frame
    A very important figure
    in the contentmath world to this day is Pythagoras. He revolutionized the math world with his theorem. Pythagoras was estimated to be born around the year 569 BC. There is very little that s known about the geniuses childhood and early years. The only outstanding physical trait that is known about Pythagoras is that he has a large birthmark that is located on his thigh area. It is thought by some people that Pythagoras has two brothers and other historians contradict that he has three brothers.
    A very influential teacher on Pythagoras’s path to mathematic greatness was Pherekydes who was believed to be the one
    of your page here.the soul keys to Pythagoras’s mathematic success. When Pythagoras was estimated to be around the age of 18 or 19 he went to the town Miletus where he learned very briefly with two great philosophers. The philosophers were Thales and his mentor Anaximander. Even though he got the chance to meet these great philosophers, he did not learn a lot of information and skills from these to mathematical minds. Even though he did not learn very much from these people he was lectured on geometry and cosmology.
    Pythagoras then took a long trip Egypt for a new start. His hometown of Samos was seized by the tyrant Polycrates and he did not want to go back to Samos. It was known that Pythagoras spent a lot of his time in Egypt visiting temples and talking to priest. Pythagoras was trying to get priesthood at many of the temples. He was denied at everyone except for the temple at Diospolis. In the year 525 BC the king of Persia at the time and one ally of Persia had invaded Egypt and the whole country fell almost without a fight. During this war Pythagoras was imprisoned and was then taken to Babylon for imprisonment.
    In the year of 520 BC Pythagoras was left out of prison because of two superior army commanders dying for the Persian army and the ruler of Persia dying shortly before. He then returned to his homeland of Samos. The man that had originally invaded Samos and died but his successor Darius was still ruling the land. Other people state that Polycrates was still in control when Pythagoras returned. After being in Samos, Pythagoras decided to take a trip to Crete. He went there to exanimate a system of laws that was there at the time.
    Pythagoras then returned to Samos and opened a small school called Semicircle. He was criticized by many people from the school for his teaching methods. He then left Samos and trekked to Southern Italy about in about the year 518 BC. When he arrived in Italy he started another school based on philosophy and religion. The school happened to be well liked and Pythagoras had many followers himself. Pythagoras joined a society in Croton called the Mathematikoi. Although they lived with the rest of the people they were believed to be vegetarians and to also not have any personal possessions. Many of the people in this society were taught by Pythagoras and went by many very strict rules.
    Of all of the work that Pythagoras had done over his years, none of it is recorded. It is not really known exactly what was taught at his schools because they learned in a circle of secrecy. Since Pythagoras had many followers there many people actually recording what he taught but Pythagoras himself never recorded anything about his findings. So many people distinguish their work with Pythagoras’s. Without these followers we would not have known anything about his revolutionary math changes in the world. It seemed to these people that Pythagoras was interested in the large principles of Mathematics like the concept of numbers and the concept of a triangle.
    In Pythagoras’s mind, numbers were the essence of all things in life and for life. In this thinking, he compare numbers with colors and virtues and he would connect numbers with many other ideas that he had. In Pythagoras’s day he believed that the Earth was a spherical object but he also believed that the planets had moved on their own directions and ways which was then disproven by the Copernican theory of the universe. He also had beiliefs of many philosophers in that time period.
    In Pythagoras’s widely known theorem which is called the Pythagorean Theorem he stated one thing. The square of the length of the hypotenuse in a right triangle equals the sum of the squares of the lengths of the two sides. Also, the square of a number is the number multiplied by it (World Book p.921). The Hypotenuse is
    the side opposite of the right angle in a triangle. The formula of the Theorem is written as c₂=a₂+b₂.
    In the formula, c is the length of the hypotenuse and b and a is the length of the other two sides of the right triangle. The reason for this discovery was because the Egyptians wanted fields with square corners that are 90 degrees. With the primitive math tools that people had in that time period. They were also trying to make a 90 degree angle. In the Pythagorean Theorem, there is known to be many Geometric proofs from many people. The Pythagoreans had created a proof to this Theorem. No one to this day knows the which proof that Pythagoras’s man created.
    After his Theorem Pythagoras was estimated to die around the date of 475 BC and no one really know’s what killed the great philosopher. Most estimate that it was old age. It changed many things in the math world in his life. He also went many different places and traveled worldwide. For some aspects math would not be what it is without Pythagoras.

    (view changes)
    8:10 am
  2. page Fermi edited ... The Atomic Energy Commission (AEC) gave Fermi a special award of $25,000 for his achievements,…
    ...
    The Atomic Energy Commission (AEC) gave Fermi a special award of $25,000 for his achievements, just before he died. The highest award given by the AEC since then is named the Fermi Prize. It is given each year "to recognize someone of international esteem, whose career has been marked by continued exceptional contributions to the development, use, or control of nuclear energy" (Enrico Fermi: Trailblazer in Nuclear Physics pg.112).
    Fermi always loved to hike in the mountains, and in the summer of 1954 while he was in Europe teaching a course on nuclear particles, he tried to enjoy his favorite activity. He didn't have his usual stamina and when he returned to Chicago doctors found that he had stomach cancer. Unfortunately, this was probably related to his work on the nuclear pile. Fermi knew his work carried risk, but he considered the outcomes so important that he took such risks. While Fermi was in the hospital, his friends found him timing the drops from the nutrient solution dripping into his veins and calculating the rate of flow, just like he loved to calculate in his experiments (Enrico Fermi: Trailblazer in Nuclear Physics, pg. 110). Fermi died in the hospital on November 29, 1954, just two months after his fifty-third birthday. Fermi was remembered by his friends as a modest, conscientious, kind, disciplined and helpful man with special talents. Fermi wanted to gain a better understanding of the physical world, but he realized that every time physicists answered one question, more questions presented themselves.
    {http://cache3.asset-cache.net/xc/50654057.jpg?v=1&c=IWSAsset&k=2&d=E41C9FE5C4AA0A14D34ADF54AB9DE9DB7DC830BA91C4B00E1BC95F90A92BE218B01E70F2B3269972}{http://16.media.tumblr.com/tumblr_kqr3swkp4i1qzn0deo1_500.jpg} {http://www.atomicnerds.com/wp-content/uploads/2008/09/enrico_fermi_id_badge.png}
    (view changes)
    4:37 am

Sunday, February 28

  1. page Fermi edited ... Fermi published his first theoretical paper in January 1921, and chose to do his research for …
    ...
    Fermi published his first theoretical paper in January 1921, and chose to do his research for his doctor's degree on X-ray diffraction. When he presented his work to the faculty committee he overwhelmed them with his knowledge. However, at the time theoretical physics was not recognized as an acceptable topic by Italian universities. Fermi received his doctorate with high honors in July, 1922, but the university refused to publish his work and considered it controversial. Later that year, Fermi published a paper that dealt mathematically with Einstein's theory of relativity. This got him recognized as an authority, while he was only twenty two years old.
    After Fermi completed his Ph.D. in physics he went back to Rome to his family. Fermi wanted to work with professor Orso Mario Corbino, who was director of the physics lab at the University of Rome. Corbino liked and respected Fermi, but there were no openings to be a professor at the university. In the first half of 1923, Fermi went to the University of Gottingen in Germany to work with Max Born, under a government awarded scholarship. He was then appointed to teach mathematics to scientists at the University of Gottingen for the academic year 1923-24. He didn't really feel like he belonged there and returned to Rome at the end of the year. Fermi worked as a teaching assistant at the University of Rome, and then had an assistantship at the University of Leiden for three months. He also taught at the University of Florence as a lecturer in mathematical physics and mechanics. It was there that he met up with his friend, Rasetti, again. During this time Fermi published a large number of papers, trying to establish himself in the field of physics.
    ...
    won the competitoncompetition to earn
    Professor Corbino built a team made up of Fermi, Rasetti, and two engineering students that brought great recognition to the University of Rome. Fermi was a slow and steady worker and could take a complicated problem and reduce it to simpler steps. The team developed long lasting friendships, but eventually they separated to learn from other laboratories. Fermi took a position to teach at the University of Michigan in 1930. This was the first time he visited the United States.
    {http://lifesciencereality.files.wordpress.com/2008/05/atom01_400x400.jpg} {http://lifesciencereality.files.wordpress.com/2008/05/atom01_400x400.jpg} {http://lifesciencereality.files.wordpress.com/2008/05/atom01_400x400.jpg}
    (view changes)
    10:49 pm
  2. page Fermi edited Enrico Fermi {http://newsletter.vonfrederick.com/images/fermi.jpg} By Scott McKean ... Rom…

    Enrico Fermi {http://newsletter.vonfrederick.com/images/fermi.jpg} By Scott McKean
    ...
    Rome, Italy. His father was an inspector on the railways, and his mother was an elementary school teacher and was the major influence on Fermi and his older brother Giulio and older sister Maria. When he
    ...
    with one of his father's
    ...
    high ability to comprehend the material and an
    ...
    talent to memorizememorize, or easily derivederive, any passage
    ...
    formulas he needed.needed to solve complicated problems. After being
    ...
    a scholarship to the school and someday
    ...
    of a theorist. Togethertheorist, so together they were
    ...
    Rasetti expelled. Fermi worked hard at his studies, but he enjoyed them very much, and he was always thinking about things and why they were the way they were, even when he was having fun.
    In 1924,
    ...
    her physics. They enjoyed traveling and raising their children together. Laura turned
    ...
    Later that yearyear, Fermi published
    ...
    as an authorityauthority, while he
    ...
    completed his Ph.D,Ph.D. in physics he went
    ...
    time Fermi was trying to increase his chances in a career by publishingpublished a large number of papers.papers, trying to establish himself in the field of physics.
    In 19251925, Fermi was
    ...
    lasting friendships, andbut eventually they
    ...
    time he came tovisited the United
    {http://lifesciencereality.files.wordpress.com/2008/05/atom01_400x400.jpg} {http://lifesciencereality.files.wordpress.com/2008/05/atom01_400x400.jpg} {http://lifesciencereality.files.wordpress.com/2008/05/atom01_400x400.jpg}
    In 19331933, Fermi made
    ...
    beta decay involvesinvolved the creation
    BETA DECAY ----> {http://www.mwit.ac.th/~Physicslab/applet_04/atom2/Betame.gif}
    ...
    this same timetime, Italy was
    ...
    was Jewish. Fermi wanted to keep his wife and family safe, but he was concerned that the government would not let him leave Italy. Secretly, Fermi wrote letters to many universities in
    ...
    United States.
    Fun Fact: When Fermi arrived in the United States, January 2, 1939, amusingly for Fermi, he had to take a arithmetic test to be granted a visa.
    ...
    By this timetime, World War
    {http://www.ultimateitaly.com/images/peoples/enrico-fermi.jpg}
    In 19411941, Fermi was
    ...
    pure uranium, and uranium oxide,
    ...
    wooden rods that were inserted
    ...
    world's first controlledcontrolled, man made, self sustainedself-sustained nuclear reaction
    FERMI'S NUCLEAR PILE ----> {http://www.anl.gov/Science_and_Technology/History/Anniversary_Frontiers/Images/15cp2.gif}
    ...
    stages of what became known as the Manhattan Project and whenProject. When any of
    ...
    Eugene Farmer. As part of this work, Fermi was
    This was my favorite fact because Fermi actually developed a bomb that had a massive amount of explosiveness. I was interested in how Fermi and his group were able to discover and design something with so much power, and how they got a huge amount of energy from something that we can't even see!
    {http://www.tangischools.org/schools/phs/think/man/FatMan.jpg} {http://www.tangischools.org/schools/phs/think/man/FatMan.jpg}
    After the warwar, Fermi went
    ...
    taught by FermiFermi, because of
    ...
    and awards through outthroughout his career,
    ...
    the negative thirteen)thirteenth) used in nuclear physicsphysics, is called
    ...
    named after Fermi.Fermi to honor his many contributions to the world.
    The Atomic
    ...
    of $25,000 for his achievements, just before he died for his achievements.died. The highest
    ...
    on nuclear particlesparticles, he tried
    ...
    returned to Chicago,Chicago doctors found
    ...
    nuclear pile. However, Fermi knew
    ...
    considered the outcomeoutcomes so important
    ...
    fifty-third birthday. Fermi was remembered by his friends as a modest, conscientious, kind, disciplined and helpful man with special talents. Fermi wanted to gain a better understanding of the physical world, but he realized that every time physicists answered one question, more questions presented themselves.
    {http://cache3.asset-cache.net/xc/50654057.jpg?v=1&c=IWSAsset&k=2&d=E41C9FE5C4AA0A14D34ADF54AB9DE9DB7DC830BA91C4B00E1BC95F90A92BE218B01E70F2B3269972} {http://www.atomicnerds.com/wp-content/uploads/2008/09/enrico_fermi_id_badge.png}
    (view changes)
    10:42 pm

More