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?

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→

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 Farenheit and degrees Celsius are still in common use in the United States.

The function C(F)=5/9(F-32) relates Celsius temperatures and Farenheit 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.

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: