# All About The Number 100

In celebration of my 100th post coming earlier this week, I figured I would discuss the number 100!!! I know, what a way to celebrate…

Applications

The number of yards in a football field.
The minimum number of yards for a par 3 hole in golf.
The number of years in a century.
The number of cents in a dollar (or pence in a pound sterling)
The boiling temperature of water at sea level, in Celsius.
The atomic number of fermium which is made by blasting plutonium with neutrons (named after the great nuclear physicist Enrico Fermi).
The number of senators in the United States Senate.
The number of tiles in a standard Scrabble set.
The basis for percentages (100% represents wholeness, purity, and perfection).
In China, tradition holds that the naming of a newborn panda must wait until the cub is 100 years old.
Pythagoreans considered 100 as divinely divine because it is the square (10^2) of the divine decad (10).
Nostradamus’ work titled “Centuries” contains 10 chapters of 100 verses each.
There are 100 squares in the 10×10 Euler (Latin or Graeco-Roman) Square. A Latin square consists of sets of the numbers 0 to 9 arranged in such a way that no orthogonal (row or column) contains the same number twice. See the image above for an example of a colorful Gaeco-Roman Square for n=10 (the capability for which was discovered by E.T. Parker of Remington Rand in 1959, disproving earlier Eulerian conjectures that a 10×10 square was impossible).

In Language

“Cem” – Portuguese
“Cent” – French
“Cento” – Italian
“Cien” – Spanish
“Honderd” – Dutch
“Hundert” – German
“Hundra” – Swedish
“Hundre” – Norwegian
“Hundred” – English
“Hundrede” – Danish
“Hyaku” – Japanese
“Miyya” – Arabic
“Sata” – Finnish
“Sto” – Croatian, Czech, Polish
“Száz” – Hungarian
“Yibai” – Chinese
“Yüz” – Turkish

Note: “Cent” is the largest number in the French language that is in alphabetical order. And funny enough, when you spell out 2*5*10=100 in French, it’s all in alphabetical order too! (deux*cinq*dix=cent)

A Mathematical Investigation

100 = 2^2 * 5^2 (factorization of 100)
100 = (1 + 2 + 3 + 4)^2
100 = 1^3 + 2^3 + 3^3 + 4^3 = 1 + 8 + 27 + 64
100 = The sum of the first nine prime numbers (2+3+5+7+11+13+17+19+23)
100 = The sum of four pairs of prime numbers (47+53, 17+83, 3+97, 41+59)
100 = The sum of the first ten odd numbers (1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19)
100 = 2^6 + 6^2 making it a Leyland Number.
100 can be expressed as a sum of some of its divisors making it a semi-perfect number.
100 is divisible by the number of primes below it (25) making it a polygonal number.
100 is divisible by the sum of its digits (in both base 10 and base 4) making it a Harshad Number.
100 is the 854th to 856th digits of pi.
100 is the 3036th to 3038th digits of phi.

In numerology, 100 equals “I LOVE WISDOM TRUTH BEAUTY”
(9) + (3 + 6 + 4 + 5) + (2 + 5 + 1 + 3 + 2 + 7) + (5 + 9 + 1 + 4 + 6 + 4)

# Archimedes: The Father of Mathematics

Summary

• Birth: c. 287 BC in Syracuse, Sicily (colony of Magna Graecia)
• Death: c. 212 BC in Syracuse, Sicily (during the Second Punic War)
• Alias(es): Archimedes of Syracuse
• Ethnicity: Greek
• Residence(s): Syracuse, Sicily; Alexandria, Egypt (during school)
• Language(s): Works were written in Doric Greek (Sicilian)
• Religion(s): Judaic Christian
• Father: Phidias/Pheidias (astronomer and mathematician)
• Mother: Unknown
• Spouse(s): Unknown
• Children: Unknown
• Relatives: King Herion II (unconfirmed), Gelon (unconfirmed)
• Acquaintances: Conon, Dositheus, Eratosthenes, Heracleides
• Class/Wealth Notes: Upper
• Institutions/Degrees: The School of Alexandria
• Profession(s): Mathematician, engineer, astronomer, physicist, inventor
• Field(s) of Study: Hydrostatics, Mechanics, Geometry, Calculus, Defense
• Famous Works: The Sand Reckoner, On the Equilibrium of Planes, On Floating Bodies, On the Measurement of a Circle, On Spirals, On the Sphere and the Cylinder, On Conoids and Spheroids, The Quadrature of the Parabola, Ostomachion, The Method of Mechanical Theorems, Book of Lemmas (Liber Assumptorum), Cattle Problem
• Legacy: “Eureka!”; known as “The Father of Mathematics”; with Newton and Gauss he is commonly referred to as one of the three greatest mathematicians who ever lived; last words were “Do not disturb my circles”;
• Cause of Death: Killed in Syracuse, Sicily during the Second Punic War despite orders from the Roman general Marcellus to leave him unharmed. The Greek historian Plutarch reported that Roman soldiers killed Archimedes to steal his scientific instruments. Another version states he was stabbed for ignoring a Roman soldier’s orders because he was too entranced in a geometrical diagram he drew in the sand.
• Notable Historian(s): Isidore of Miletus, Eutocius, Plutarch, Polybius, Thābit ibn Qurra (Arabic translator), Gerard of Cremona (Latin translator)

Archimedes’ Principle & The First Law of Hydrostatics

Story: Archimedes was tasked to determine if the new crown made for King Herion II was made of solid gold. While taking a bath, he observed the level of water in the tub rise as he got in… leading to his “Eureka!” moment regarding density and displacement.

Science: A body immersed in a fluid experiences a buoyant force equal to the weight of the fluid it displaces. Therefore Archimedes could immerse the crown in water, measure the amount of water displaced, divide it by the weight of the crown, and arrive at the density of the crown.

Impact: Hydrostatics, or the study of the mechanical properties of liquids at rest, was born. Archimedes’ Principle regarding buyancy and density is used throughout science today. It’s used in the building of ships, other industrial manufacturing, and really any type of engineering. Without it, well, we might be “screwed” (see Archimedes’ other works below).

Other Works

• Archimedes’ Screw – This consists of a long screw enclosed in a cylinder. With tilted so that its bottom tip is placed in the water, turning the screw pushes water up the screw and out the top. This was used to bilge water out of large ship he designed, the Syracusia.
• Law of the Lever – Achimedes supplied the first real scientific explanation of how levers work in his work titled On The Equilibrium of Planes (although he certainly did not invent levers).
• Method of Exhaustion and Pi – Archimedes used the “method of exhaustion” to determine approximate areas and volumes of circles. It involves drawing one polygon outside of a circle, and inscribing a similar polygon on the inside of the circle. Since the area of a polygon (at that time) could be worked out more easily than a circle, Archimedes would determine the areas of the polygons, continuously adding more sides to the polygons, computing the new areas, and estimate the area of the circle which falls between those of the inner and outer polygons. This helped him determine an approximation of pi which he set at somewhere between 3.1429 and 3.1408.
• Spheres and Cylinders – Archimedes, through the use of several means, proved that a sphere had two-thirds the volume and surface area of a cylinder that circumscribes the sphere.
• Engineering Feats – Archimedes engineered and built several machines, based on the physical properties and relationships he had proven, to help defend Syracuse from the Roman assault. These included giant pulleys and catapults that would lift ships out of the water and shake them up, destroying them (check out the “claw of Archimedes”). He also built a giant mirror that focused the sunlight onto a ship to burn it.