Language is based in threes. Sender, message, receiver. Subject verb object. A language involves a semantic system, a phonological system, and a syntactic system. Phonetics study the sounds of languages from three basic points of view.

Do you recall studying for your exams? You probably do. But do you remember how you studied, how you memorized French words or the year of the American civil war? Now, that’s probably harder. As a teenager, Ricardo Lieuw On was packing groceries when he knew what he wanted to study: he wanted to learn about learning. He picked up a study in psychology and learned how to reduce his learning time from 3 hours to 1 hour on the same piece of content. He gained the same knowledge in 200% less time. And specially for TEDxHaarlem, he shares the secret of his technique. This talk was given at a TEDx event using the TED conference format but independently organized by a local community. Learn more at https://www.ted.com/tedx

Each person in grammar represents a different perspective or point of view (POV) in a narrative. First person includes the speaker (English: I, we, me, and us), second person is the person or people spoken to (English: you), and third person includes all that are not listed above (English: he, she, it, they, him, her, them, the people). It also frequently affects verbs, and sometimes nouns or possessive relationships.

First Person POV (I am experencing it) – “My heart leaped into my throat as I turned and saw a frightening shadow.”

Second Person POV (putting you into the story) – “You turn and see a frightening shadow.”

Third Person POV (about a group) – “They turned and saw the frightening shadow.

The First-Person Point of View

When you write or speak in the first person, you are telling your own thoughts or ideas or those of a group you belong to. The following are examples of self-directed statements:

I arrived at the party before the other guests did. There was a ticket waiting for me at the counter. This has always been a favorite movie for us.

The Second-Person Point of View

The second person addresses the audience whether it is one person or many people:

You are my best friend. You can feel good about the way you played today. You all deserve credit for the company’s performance this quarter.

The Third-Person Point of View

We will use the third person to refer to someone or something that is either not us or not an audience we’re addressing:

After leaving late from the meeting, she had to run to catch the bus. They should be careful when walking around that puddle. It wouldn’t start because the battery was dead.

The following general guidelines might be helpful in making choices

First-person points of view tend to be more descriptive and individual.

The second person is usually recognized as more intimate, immediate, and persuasive.

Third-person perspectives create more distance and often feel more rational.

By experimenting with different voices in your writing, you’ll learn to use each effectively as it suits your intentions. An essay may be most powerful in the first person, for example, while a science-fiction short story might explore new possibilities in the third person.

The three main types of third-person point of view

By Richard Nordquist Updated on May 30, 2019

In a work of fiction or nonfiction, the “third-person point of view” relates events using third-person pronouns such as “he,” “she,” and “they.” The three main types of third-person point of view are:

Third-person objective: The facts of a narrative are reported by a seemingly neutral, impersonal observer or recorder. For an example, see “The Rise of Pancho Villa” by John Reed.

Third-person omniscient: An all-knowing narrator not only reports the facts but may also interpret events and relate the thoughts and feelings of any character. The novels “Middlemarch” by George Eliot and “Charlotte’s Web” by E.B. White employ the third-person-omniscient point of view.

Third-person limited: A narrator reports the facts and interprets events from the perspective of a single character. For an example, see Katherine Mansfield’s short story “Miss Brill.”

In addition, a writer may rely on a “multiple” or “variable” third-person point of view, in which the perspective shifts from that of one character to another during the course of a narrative.

A Pythagorean triple consists of three positive integers a, b, and c, such that a^{2} + b^{2} = c^{2}. Such a triple is commonly written (a, b, c), and a well-known example is (3, 4, 5). If (a, b, c) is a Pythagorean triple, then so is (ka, kb, kc) for any positive integer k. A primitive Pythagorean triple is one in which a, b and c are coprime (that is, they have no common divisor larger than 1). For example, (3, 4, 5) is a primitive Pythagorean triple whereas (6, 8, 10) is not. A triangle whose sides form a Pythagorean triple is called a Pythagorean triangle, and is necessarily a right triangle.

The name is derived from the Pythagorean theorem, stating that every right triangle has side lengths satisfying the formula a^{2} + b^{2} = c^{2}; thus, Pythagorean triples describe the three integer side lengths of a right triangle. However, right triangles with non-integer sides do not form Pythagorean triples. For instance, the triangle with sides a=b=1 and c=2 is a right triangle, but (1,1,2) is not a Pythagorean triple because 2 is not an integer. Moreover, 1and 2 do not have an integer common multiple because 2 is irrational.

Pythagorean triples have been known since ancient times. The oldest known record comes from Plimpton 322, a Babylonian clay tablet from about 1800 BC, written in a sexagesimal number system. It was discovered by Edgar James Banks shortly after 1900, and sold to George Arthur Plimpton in 1922, for $10.

One example of a Pythagorean triple is a=3, b=4, and c=5: Ancient Egyptians used this group of Pythagorean triples to measure out right angles. They would tie knots in a piece of rope to create 3, 4, and 5 equal spaces. Three people would then hold each corner of the rope and form a right triangle!

right triangles during the construction process to help determine the slope of the pyramid. The Pythagorean Theorem states that given a right triangle with sides of length a and b respectively and a hypothenuse of length c, the lengths satisfy the equation a^{2} + b^{2} = c^{2.}

When searching for integer solutions, the equation a^{2} + b^{2} = c^{2} is a Diophantine equation. Thus Pythagorean triples are among the oldest known solutions of a nonlinear Diophantine equation. The simplest linear Diophantine equation takes the form ax + by = c, where a, b and c are given integers. The solutions are described by the following theorem: This Diophantine equation has a solution (where x and y are integers) if and only if c is a multiple of the greatest common divisor of a and b.