Mathematics uses many concepts in threes. The first structure mathematically is a triangle. There are acute, right, and obtuse angles. Trigonometry is the study of the relationship of the sides of a triangle. Have your heard of Pascal's Triangle?

Four triangular faces along with six edges meeting at four vertices together describe the regular tetrahedron. The tetrahedron is the root of all entanglements that shape the perceivable bonds that hold life together in this dimension. The regular tetrahedron can be found at the source of all three-dimensional forms and is fundamental in the creation of all patterns and holographic configurations.

“All of the definable structuring of Universe is tetrahedrally coordinate in rational number increments of the tetrahedron. By tetrahedron, we mean the minimum thinkable set that would subdivide the Universe and have the interconnectedness where it comes back upon itself. The basic structural unit of physical Universe quantation, tetrahedron has the fundamental prime number oneness.”

Buckminster Fuller

“Within it (tetrahedron) lies the energy that holds all life together. The bonds that hold atoms, particles and molecules together, all the way down to nanoparticles and all the way up to macroparticles, are tetrahedral. Everything that exists as you conceive of it in a 3-dimensional world, is held together by these tetrahedral bonds.”

Buckminster Fuller

“The tetrahedron is a form of energy package. The tetrahedron is transformable…All of the definable structuring of Universe is tetrahedrally coordinate in rational number increments of the tetrahedron.”

Buckminster Fuller

“Two Triangular Energy Events Make Tetrahedron: The open-ended triangular spiral can be considered one “energy event” consisting of an action, reaction and resultant. Two such events (one positive and one negative) combine to form the tetrahedron.”

There are three possible geometries of the universe: closed, open and flat from top to bottom. The closed universe is of finite size and, due to its curvature, traveling far enough in one direction will lead back to one’s starting point. The open and flat universes are infinite and traveling in a constant direction will never lead to the same point.

Universe with positive curvature. A positively curved universe is described by elliptic geometry, and can be thought of as a three-dimensional hypersphere, or some other spherical 3-manifold (such as the Poincaré dodecahedral space), all of which are quotients of the 3-sphere.

Some math conjectures and theorems and proofs can take on a profound, quasi-religious status as examples of the limits of human comprehension. TREE(3) is one of those examples.

“You’ve got all these physical processes going on in the universe all around you. None of them are anything compared to TREE(3),” says University of Nottingham mathmatics professor Tony Padilla in a new episode of the wonderful YouTube series Numberphile.

What do Euclid, 12-year-old Albert Einstein, and American President James A. Garfield have in common?

They all came up with elegant proofs for the famous Pythagorean theorem:

In mathematics, the Pythagorean theorem, also known as Pythagoras’s theorem, is a fundamental relation in Euclidean geometry among the three sides of a right triangle. It states that the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

What do Euclid, 12-year-old Albert Einstein, and American President James A. Garfield have in common?

Beneath three glass bell jars, in a locked vault in the basement of a highly secure facility outside Paris, sits the world’s most important kilogram.

Ever since 1889, when the General Conference on Weights and Measures (CGPM) made the imperious pronouncement, “this prototype shall henceforth be considered to be the unit of mass,” this platinum and iridium cylinder has served as the standard by which all other kilograms are measured, from the weights on a high-tech lab scale to the plastic discs high schoolers use in chemistry class. It’s known as “le Grand K,” and it’s afforded the security and scrutiny befitting such a fancy title. Even the researchers who work with it can’t touch it, lest their fingertips wipe away atoms or leave residue on the gleaming surface. The vault containing the cylinder can only be opened by gathering three custodians carrying three different keys, and that’s happened fewer than a dozen times in the kilogram’s 127-year history. Continue reading Scientists just got one of the best measures yet of a fundamental of physics

f is the outer function; g is the inner function. `Suppose f(x) = x-2 and g(x) = x2. (a) Find fog and gof. (fog)(x) = f(g(x)) = f(x2) = x2-2.

In 1954, the tenth general conference on weights and measures adopted the Kelvin K as the basic unit for measuring all international weights and measures. While the kelvin is the standard unit, degrees Fahrenheit and degrees Celsius are still in common use in the United States.

The function C(F)=5/9(F-32) relates Celsius temperatures and Fahrenheit Temperatures. The function K(C)= C + 273.15 relates celsius temperatures and kelvin temperatures.

Let’s convert Fahrenheit to Kelvin. The composition of the function K with the function C is

K(C(F)) = C(F) + 273 = (5/9)(F-32) + 273

Since C converts Fahrenheit to Celsius and K converts Celsius to Kelvin, the composition will convert Fahrenheit to Kelvin.

In English:

To convert Fahrenheit to Celsius, subtract 32 from the Fahrenheit temperature and then divide your answer by 1.8.

To convert from Celsius to Fahrenheit, multiply the Celsius temperature by 1.8 and then add 32 to your answer.

If you’re trying to convert Celsius to Kelvin, just add 273.15 to the Celsius temperature.

At what temperature are Fahrenheit and Celsius the same?

Let’s solve a system of linear equations graphically then algebraically.

Graphing solution:

Algebraic solution:

The formulas for converting between degree Celsius and degree Fahrenheit are:

°F = (°C * 9/5) + 32
°C = (°F – 32) * 5/9

To find the temperature when both are equal, we use an old algebra trick and just set ºF = ºC and solve one of the equations.

°C = (°C * 9/5) + 32
°C – (°C * 9/5) = 32
-4/5 * °C = 32
°C = -32 * 5/4
°C = -40

The Rule of Three is a Mathematical Rule that allows you to solve problems based on proportions. By having three numbers: a, b, c, such that, ( a / b = c / x), (i.e., a: b :: c: x ) you can calculate the unknown number. The Rule of Three Calculator uses the Rule of Three method to calculate the unknown value immediately based on the proportion between two numbers and the third number.

The working of the Rule of Three Calculator can be expressed as follows: