The Pythagorean Triples will represent three positive integers that will satisfy the formula a^2+b^2=c^2 thus the square of the hypotenuse (longest side) c will be equal to the square of the sides a and b. 9 + 16 = 25 3 4 5 Therefore: 3^2+4^2=5^2 9+16=25 Thus (3,4,5) are Pythagorean triples. FIRST DERIVATION OF PYTHAGOREAN TRIPLES: Generally when trying to derive the Pythagorean triple, we begin by finding the algebraic sum of the squares of the two smaller numbers which in turn will be used to derive the square of the hypotenuse that satisfy the condition of the square of the two smaller numbers. The square of one of the Pythagorean Triples can either be an even or an odd number. Thus supposing a^2 is the square of one of the Pythagorean Triples and b is the second triple.
Golden Ratio in Nature Introduction The Golden ratio is represented with the Greek letter phi ( or ) and has a value of approximately 1.618. The Golden ratio creates a special fascination that has caught the attention of mathematical minds for 2,400 years. The Golden ratio can be found in many areas such as art, architecture and nature, making it a very special value that I have found interest in exploring. Mathematics of the Golden ratio The Golden ratio is represented as a mathematical ratio with special properties. In this section we will be discussing about the mathematical calculations behind the Golden ratio.
Find the area under the standard normal curve between z = -1.65 and z = 0. Answer: The area may be represented as . Since the normal curve is symmetric, then 3. Find the area under the standard normal curve between z = -1.65 and z = 1.96. Answer: The area may be represented as.
Some roulette players use a sequenced betting system. The set of numbers in the sequence determines the size of the bet in a system known as the Fibonacci roulette betting system. As you might have noticed, the name is taken from one of the greatest mathematicians of the Middle Ages. That's because this betting system is actually based on his homonymous number sequence—the Fibonacci numbers. A Bit of History Leonardo Fibonacci, also known as Leonardo of Pisa, presented to the world a sequence of numbers in his book Liber Abaci, in the year 1202.
The concept is a singularity based approach. The explosion of a miniature particle in the early universe is what the Big Bang is based upon. It provides the scientific community with assistance in solving the answers of the primitive space. Similarly Hubble space telescope solidifies the fact of Big Bang approach. Recently experiments of Higgs Boson in Large hadron collider, comes out handy in explaining the creation of universe from singularity approach.
Babylonians might have invented mathematics; however, Abu Jaafar Mohammad Ibn Mousa Al Khwarizmi was the brilliant mathematician who perfected it (Kéchichian, 2013). He was undoubtedly one of the greatest mathematicians in the world noting one of his greatest works to be the “Hisab Al Jabr wal-Muqabalah” (The Book of Integration and Equation), which introduced the use of Indo-Arabic numerals that, over time, came to be known as algorithms (Kechichian, 2013). He was noted for many achievements including the invention of "aljabr" (Algebra) and introduced many different mathematical deductions and mechanisms that improved our knowledge and understanding in the present and later in the future. Very little is known about Al Khawarizmi's life;
In 400 B.C. Democritus claimed that atoms are a single material formed into varied shapes and sizes. John Dalton found that atoms of different elements are different and ones of the same
These numbers are all successive numbers in the Fibonacci sequence. These numbers can be applied to the proportions of a rectangle, called the Golden rectangle. Those equations successfully demonstrate the importance of mathematics in the world. The value in math is absolute because it is measured using equations. Many buildings and artworks have the Golden Ratio in them too, such as the Parthenon in Greece.
The turning and spinning solar system with vast collection of stars composes the Milky Way galaxy. It is only one of the billions of galaxies which make up our universe. From this, we can tell that the universe is really big, and was it said that it’s still getting bigger and expanding. A theory suggests that the universe used to be smaller and much smaller than the smallest part of an atom. It was incredibly smaller until everything happened, everything expanded.
Issuers are in general interested in contracts with such an embedded option because it allows them to redeem the bond when the conditions of the financial market are in their favour. Therefore, the call option is mainly beneficial for the issuer, that’s why it’s less expensive than a bond without a call feature . The standard approach to price callable bonds was based on interest rate dynamics. For example a trinomial