Origins of Zero

We're used to seeing it as a nothing, or even part of the code on a barcode label . But zero is probably the most complicated number in existence. It has stumped amateur math students as well as genius mathematicians since the concept of math was first developed.

Zero first appeared in the middle of the 2^nd millennium BCE when the Babylonian math system included it. Ancient Greeks were unsure about the existence of the number. It wasn’t until 9^th century India that zero began being regarded as a real number, and not a symbol for separating positive and negative numbers.

Why Dividing by Zero Can Get You into Trouble

Put simply, you run into trouble dividing by zero because zero actually can’t be divided by anything. However, people assume that you actually get a result when you divide by zero because they assume that the answer is zero. They forget the distinction - an invalid math operation is invalid, and it certainly does not equal zero.

Is Zero Either Positive or Negative?

Since zero is the marking point between negative and positive numbers, it’s neither. It has no real value so it can’t be positive or negative.

Is Zero an Even or Odd Number?

Zero is an even number. Even numbers are any number that is evenly divisible by 2. As zero divided by 2 is zero, it’s an even number.

Is 1 a Number or Just a "Unit" for Counting?

It’s actually both. One is used as both a real number as well as a unit for counting. A unit of counting means most default measurements for things in mathematics. For example, in a line segment, the default unit length is always 1.

Origin of Infinity and its Symbol

The term “Infinity” refers to several concepts. In philosophy, it means something going on forever, without end. In math, it’s used as a real number. The symbol of infinity is a sideways figure 8. However, the symbol is somewhat of a mystery because its precise origin is unknown. Though it existed many years before, it is most commonly credited to John Wallis in 1665 when he wrote De sectionibus conicis.

Other Apparent Difficulties with Zero

Most mathematicians note that what makes zero so difficult to deal with is the fact that it’s not even really a true number. They propose that it’s just a concept. It’s a way to begin measuring a set of numbers, but since zero is technically nothing, it remains a concept rather than anything concrete.

Descartes' Representations of Numbers

Rene Decartes’ mathematical work is some of the most influential ever. His work applying infinitesimal calculus to the tangent line problem allowed that branch of mathematics to rapidly progress, eventually allowing Newton to make his mark on calculus. His rule of signs is also the most widely-used method of determining the number of negative and positive roots of a polynomial. This representations of numbers changed how math was done forever.

Pi Day & History Of Pi π

Pi Day

Pi Day is celebrated on March 14th (3/14) around the world. Pi (Greek letter “π”) is the symbol used in mathematics to represent a constant — the ratio of the circumference of a circle to its diameter — which is approximately 3.14159.

Pi has been calculated to over one trillion digits beyond its decimal point. As an irrational and transcendental number, it will continue infinitely without repetition or pattern. While only a handful of digits are needed for typical calculations, Pi’s infinite nature makes it a fun challenge to memorize, and to computationally calculate more and more digits. Many of us measure the value of 22/7 as π .
but actually the value of 22/7 is nearly o.oo13 more than the actual value of π .

History

Antiquity

The Great Pyramid at Giza, constructed c. 2589–2566 BC, was built with a perimeter of about 1760 cubits and a height of about 280 cubits; the ratio 1760/280 ≈ 6.2857 is approximately equal to 2π ≈ 6.2832. Based on this ratio, some Egyptologists concluded that the pyramid builders had knowledge of π and deliberately designed the pyramid to incorporate the proportions of a circle. Others maintain that the suggested relationship to π is merely a coincidence, because there is no evidence that the pyramid builders had any knowledge of π, and because the dimensions of the pyramid are based on other factors.

The earliest written approximations of π are found in Egypt and Babylon, both within 1 percent of the true value. In Babylon, a clay tablet dated 1900–1600 BC has a geometrical statement that, by implication, treats π as 25/8 = 3.1250. In Egypt, the Rhind Papyrus, dated around 1650 BC, but copied from a document dated to 1850 BC has a formula for the area of a circle that treats π as (16/9)2 ≈ 3.1605.

In India around 600 BC, the Shulba Sutras (Sanskrit texts that are rich in mathematical contents) treat π as (9785/5568)2 ≈ 3.088. In 150 BC, or perhaps earlier, Indian sources treat π as

≈ 3.1622.

Two verses in the Hebrew Bible (written between the 8th and 3rd centuries BC) describe a ceremonial pool in the Temple of Solomon with a diameter of ten cubits and a circumference of thirty cubits; the verses imply π is about three if the pool is circular. Rabbi Nehemiah explained the discrepancy as being due to the thickness of the vessel. His early work of geometry, Mishnat ha-Middot, was written around 150 AD and takes the value of π to be three and one seventh.