Michael Rice
Applying math to real life
September 3, 2010
Obituary for Archimedes of Syracuse
Archimedes was born in Syracuse, Italy in 287 B.C. His father was Pheidias, who happened to be an astronomer. He studied at Alexandria, Egypt. He was also close friends with the King of Syracuse. He died in 212 B.C. Archimedes performed numerous geometric proofs using the rigid geometric formalism outlined by Euclid, excelling especially at computing areas and volumes using the method of exhaustion. He was especially proud of his discovery for finding the volume of a sphere, showing that it is two thirds the volume of the smallest cylinder that can contain it. At his request, the figure of a sphere and cylinder was engraved on his tombstone. In fact, it is often said that Archimedes would have invented calculus if the Greeks had only possessed a more tractable mathematical notation. By inscribing and circumscribing polygons on a circle. Archimedes was also an outstanding engineer, formulating Archimedes' principle of buoyancy and the law of the lever. Legend has it that Archimedes discovered his principle of buoyancy, which states that the buoyancy force is equal to the weight of the liquid displaced, while taking a bath, upon which he is supposed to have run naked through the streets of Syracuse shouting "Eureka!" (I have found it). Archimedes is also purported to have invented the Archimedean screw. Some of Archimedes's geometric proofs were actually motivated by mechanical arguments which led him to the correct answer. During the Roman siege of Syracuse, he is said to have single-handedly defended the city by constructing lenses to focus the Sun's light on Roman ships and huge cranes to turn them upside down. When the Romans finally broke the siege, Archimedes was killed by a Roman soldier after snapping at him "Don't disturb my circles," a reference to a geometric figure he had outlined on the sand.

...Dominic Sachs
2nd block
Archimedes
Inventions of ArchimedesArchimedes area of expertise was inventions and coming up with great ideas. He was a very smart person, and had invented some useful inventions for human kind for what is still used today. BC. He was a physicist, engineer, inventor, astronomer and a Greek mathematician. Archimedes is one of the greatest math mathematicians of all time. He has been given credit for the invention of the lever even though it was used thousand of years before his time despite the fact that he did not invent it. He only gave an explanation of the principal involved in his work. Once He had made the statement “If I were to have a place to stand, I would be able to move the entire earth”.
Another invention Archimedes had invented was the Archimedes screw. This invention helps to bring water from lower areas to higher grounds by a rotating screw inside a tube constantly. The water is forced out the tube even though the water is at lower ground. This invention is also used today.
Also an interesting invention Archimedes invented was the Heat Ray. This was used to destroy enemy ships by catching a part of the ship on fire then having it burn all the way down. People have tested this invention out to see if it was true for example, in 1973 a Greek scientist Ioannis Sakkas but had failed. In 2006 the Mythbusters had...

...Michael Gray
Biography of a Mathematician
Archimedes, one of the greatest mathematicians, engineers, physicist, inventors, and astronomer's in history. Ranked with the likes of Isaac Newton and Carl Gauss, Archimedes contributions to math include the area of geometry, number theory, algebra, and theorems of plane.
Birth
Archimedes was born in Syracuse, Greece on the island of Sicily in 287 BC. Son of Pheidias, a well-known astronomer, and research showing that Archimedes is thought to be a relative of King Hiero II. King Hiero II questioned a crown made for him. Archimedes studied the crown and discovered the purity of the gold in the crown. Archimedes was sitting in a bath house, watching water running from the crown of King Hiero II, observing the pattern of the water, Archimedes figured the excess of bulk with the introduction of certain alloys can be measured by placing the crown with an equal weight of gold in a separate container filled with water. This observation showed the difference of overflow; and the birth of the Archimedes Screw.
Education
Phidias, Archimedes father did not want his son in Syracuse during the times of war, living a life of luxury, Archimedes was allowed o peruse the finer things in life, education. Greek families at the time wanted children to be knowledgeable,...

...
Antonio Resendiz
Mrs. Frenzel
05/08/15
Algebra II
ArchimedesArchimedes was born in the city of Syracuse on the island of Sicily in 287 BC. He was the son of an astronomer and mathematician named Phidias. Some historians say that his family belonged to the nobility of Syracuse, and that his family was in some way related to that of Hiero II, King of Syracuse. Syracuse was the cityArchimedes live, Syracuse was a hub of commerce, art and science. As a youth in SyracuseArchimedes developed his natural curiosity and penchant for problem solving. When Archimedes was done learning new things in Syracuse, he then decided to traveled to Egypt in order to study in Alexandria. He made this decision because Alexandria had earn a reputation for great learning and was highly advanced society by Archimedes standards.
Archimedes was also an engineer, inventor and astronomer.Archimedes was best known throughout most of history for his military innovations like his siege engines and mirrors to harness and focus the power of the sun, as well as levers, pulleys and pumps . But his most famous invention was his screw pump, known as the Archimedes' Screw. This innovation is still use in many parts of the world for irrigation. But what really made Archimedes...

...Archimedes of Syracuse (287 BC – 212 BC) was a Greek mathematician, physicist, engineer, inventor, and astronomer. Archimedes is generally considered to be the greatest mathematician of antiquity and one of the greatest of all time. He used the method of exhaustion to calculate the area under the arc of a parabola with the summation of an infinite series, and gave a remarkably accurate approximation of pi. He also defined the spiral bearing his name, formulae for the volumes of solids of revolution, and an ingenious system for expressing very large numbers. Archimedes had proven that the sphere has two thirds of the volume and surface area of the cylinder and regarded this as the greatest of his mathematical achievements.
Some of Archimedes' greatest writings are preserved on a palimpsest which has been rediscovered and properly studied only since 1998.
Although Newton may have been the most important mathematician, and Gauss the greatest theorem prover, it is widely accepted that Archimedes was the greatest genius who ever lived.The works of Archimedes were written in Doric Greek, the dialect of ancient Syracuse.[53] The written work of Archimedes has not survived as well as that of Euclid, and seven of his treatises are known to have existed only through references made to them by other authors. Pappus of Alexandria mentions On Sphere-Making...

...Title: Density, Alcohol Content and the Archimedes Principle
(Performed 09/11/13)
Report submitted by:
Purpose: Part I was to examine three different objects of the same material in order to identify the type of metal. We used the water displacement method and the buoyancy method according to Archimedes Principle. Part II was to find the density of ethanol by mass. We used a 25.0mL graduated cylinder and a 25.00mL volumetric flask to measure the volume. We used two different pieces of glassware to determine the most accurate density of ethanol by mass since the measurement of volume is variable.
Procedure: As stated in lab manual pages 23-24.
Data and results for part I: Density and identification of a solid:
Calculated Density Using the Water Displacement Method
Mass of object (g) Initial volume (mL) Final volume (mL) Volume of object (mL) Density (g/mL)
Trial 1 17.635 61.9 64.0 2.1 8.4
Trial 2 21.707 71.9 76.0 4.1 5.3
Trial 3 16.755 67.8 69.8 2.0 8.4
d=m / V
Trial 1: d= 17.635g/2.1mL = 8.4g/mL
The average of the calculated density: 7.4g/mL
The calculated standard deviation: 1.8
We identified the metal as Zinc (7.14g/mL). However we believe the calculated density of trial 2 seemed inconsistent with the other two trials. Therefore we believe that the...

...MEASUREMENT OF PHYSICAL PROPERTIES: DENSITY
Introduction
According to the definition Density is the physical property that allows us to compare the mass of substances for a specific volume. In this Lab activity that took place in Deree College, Agia Paraskevi Campus we deal with the density of solids and density of liquids. The main purpose of this experiment is to understand what in reality density means, how we can measure it, how useful it is, what is the difference between density of solids and liquids, if the measurements that we did are been accurate and how we can calculate the percentage errors.
materials
3 different metals
A) copper
B) iron
C) aluminum
- 3 Different liquids
A) Water
B) Olive oil
C) Alcohol
- Balance
- Cylinders of 25ml, 100ml
- Calculator
DATA/RESULTS
In this Lab activity we saw the differences between the density of solids and the density of liquids.
Firstly we obtained three different solids a piece of aluminum, a piece of copper and a piece of iron, and we measured their masses by using the balance. Also, we measured their volume by using a cylinder with distilled water, then we have measured the volume, and then we put in the metal and recorded the total volumes. After that we calculated each density and we recorded the average density (by classmates)....

...purpose of the lab was to determine density of both regular and irregular shaped objects. Throughout the lab I found out that both of the small and large silver rod, do not have the same density, and also found out that the gold rod is not real gold.
My hypothesis is that since, the large and small silver rod has about the same density I believe that they would have about the same amount of volume. They both might displace the same amount of water on the graduated cylinder.
The Materials we used throughout the lab was:
Metal rods (Gold & Silver)
Wooden block
Water
Scale
Ruler
Graduated cylinder
Procedure thought out the lab:
1. First step we did was get the materials and went to out stations with our partners.
2. Second me and my partner measured the mass of the metal rods and the wooden block and recorded them on the worksheet.
3. After we filled up the graduated cylinder with water and dropped one of the metal rods and the water, the water amount that increased in the cylinder was the volume of the rode that was placed in.
4. We continued to measure and record the volume of each of the metal rods the same way as the first.
5. We measured the length, width, and height of the wooden block and recorded it. Then multiplied them altogether to get the volume of the block.
6. After gaining the measurements of the mass and volume of the metal rods and the wooden block, me and my partner then used both the mass and volume to...

...Physics 141 Archimedes --1
ARCHIMEDES’ PRINCIPLE AND SPECIFIC DENSITY
GOAL: To investigate buoyant force and Archimedes’ principle. To measure the specific density of several materials. INTRODUCTION: Try pushing down on a basketball in water and you feel the buoyant force that makes the ball float. As more of the ball is pushed beneath the water, the upward force becomes greater. One could make a first guess (Hypothesis #1) that the buoyant force increases with the submerged volume of the object. A more mathematical guess (Hypothesis #2) might be that the upward or buoyant force, B, is proportional to the submerged volume, Vsub, of the object. feathers, is in fact a statement that the density of lead is greater than the density of feathers. Recall for a homogeneous object with a volume, V, and a density, D, has a mass, m:
(4)
Thus the statement that lead is heavier than feathers, is correct if equal volumes of the two materials are compared. For many practical applications, it is important to be able to compare densities of various materials. One could compile a list that compares the density of everything to density of everything else, but it is easier to compare the densities of everything to just one substance, water. Water is chosen because it is very readily available and is frequently used in...

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