Friday, June 19, 2009

The Konigsberg Network

Do you know that geometry has been applied to problems in designing telephone and communication system, transportation connection and computer connection? these design problems can often be represented by a network consists of a set of vertices and the connecting paths between them

One of the most famous network problems was noted in the 16th century in konigsberg, Prussia(Prussia covered the teritory under the former german empire). The town comprised two island in the middle of a river. The town was connected by 7 bridges which crossed the river. The question was whether person could plan a walk, starting any where, so that all 7 bridges could be crossed without crossing the same bridge twice.

Leonhard Euler first studied this problem in 1735. Here is Euler's approach to the problem: Euler began by redrawing the map so that 4 areas of land were represented by points with seven lines to represent the bridges. That konigsberg problem can now restated as follows: Given 4 distinct vertices. try to draw a continuous path from one vertex to another, without retracing a previous drawn path.

Euler discovered that such a network can only be drawn if one of these conditions are true:

1. there are exactly two vertices with an odd number of paths leading from them.

2. All vertices have an even no. of paths leading of them.

Did you Know?

Higantes Fesival

...that the people of Angono, Rizal celebrate their town fiesta on November 22 -23 of every year? Angono celebrate it in honor of San Clemente, patron Saint of fishermen. whose image, shining brilliantly in papal vestment, is carried out by male devotees during a procession accompanied by pahadores (devotees dressed in colorful local costumes or fishermen's clothes, wooden shoes and carrying boat paddles, fish nets or traps)and higantes , Giant paper mache images.

...That the street event culminates in a fluvial procession in Laguna de bay amidst merry making that continues until the image is brought back to the church.

...That the Higantes, which had color and merriment to Angono town fiesta, are giant paper mache effigies measuring 4- 5 feet in diameter and 10-12 feet in height.

The Origin of Nuclear Weapons

The First Atomic Bomb

Albert Eintein's equation,E=mc square paved the way for the creatin of the first atomic bomb. Through the studies of scientists around the orld about radioactivity, the possibility of creating a weapon of unimaginable explosive power became imminent.
As early as 1934, a group of American scientists was already discussing the possibility of of creating nuclear weapon. European scientists were also on the way to discovering the powerful effects of the nuclear bomb.


five years later, four scientists found the key to nuclear energy-Otto, Lisa Meitner, Fritz Strassman, and Otto Frisch. They discovered that a neutron,when placed into a uranium nucleus through radioactive bombardment, can split the nucleus into nuclei,barium and krypton, with a massive outburst of energy.
But the war in Europe forced these brilliant scientists to sail to the USA.
There they joined other groups of American scientists. On December 6, 1941 the day before the bombing of Pearl Harbor, American President Franklin D. Roosevelt approved the plan for all-out effort in atomic research.
It was Enrico Fermi who completed and experiment on how nuclear fission could be started, sustained and stopped. Together with Robert Oppenheimer and other notable figures, they carried out the Manhattan Project. They worked in an atmosphere urgency, excitement and secrecy.
In july 16, 1945, the first plutonium bomb was tested at Alamogordo Airbase in New Mexico. The test proved that the possibility of a nuclear war was at hand. The result of the succesful test were sent to the president who was in the meeting in Potsdam, negotiating the occupation of germany.
On the 26 of july of the same year, President Roosevelt sent a memorandum to the Hapanese to surrender or else face harsh consequences. But because of pride and determination, the Japanese rejected the ultimatum.
By the first week of August, the two bombs, "The little Boy" (Hiroshima Bomb) and "The Fat Man" (nagasaki bomb) were ready to be drop.