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- In mathematics, the equal sign can be used as a simple statement of fact in a specific case (" x = 2 "), or to create definitions (" let x = 2 "), conditional statements (" if x = 2, then... "), or to express a universal equivalence (" (x + 1)2 = x2 + 2x + 1 ").
en.wikipedia.org/wiki/Equals_sign
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Dec 10, 2020 · So, “all right angles are equal,” what’s the deal with that? First of all, what does “right angle” mean? Euclid defines it in Definition 10. Draw a line. Consider the space on one side of the line. Cut that space in half with another line. That’s a right angle. A right angle is half the space on one side of a line.
$$:=$$ is the commonest symbol to denote "is equal by definition." Note that $$\equiv$$ is used to denote an algebraic identity: this means that the equation is true for all permitted values of its variables.
In mathematics, equality is a relationship between two quantities or, more generally, two mathematical expressions, asserting that the quantities have the same value, or that the expressions represent the same mathematical object.
- Euclidean Rigour
- Euclid's Postulates
- Euclid and Physics
- Euclid and Philosophy
- Euclid in Art and Architecture
- About This Article
Many important later thinkers believed that other subjects might come to share the certainty of geometry if only they followed the same method. René Descartes, for example, said that if we start with self-evident truths (also called axioms) and then proceed by logically deducing more and more complex truths from these, then there's nothing we could...
Before we look into the influence of Euclid's geometry, let's have a look at the assumptions, or postulates, he built this geometry on. The first four are shown in the box on the right. They are straightforward and nobody in their right mind would doubt them. But there is also a fifth one, called the parallel postulate: If a straight line that fall...
Euclid never talked about the spacehis geometric shapes live in, but it appears that he implicitly assumed it to be an infinite expanse that's the same in all directions and in which every point is just like every other point. Later thinkers, especially starting in the Renaissance, talked a lot about space. And they agreed with these earlier assump...
Philosophy was equally permeated by Euclid's ideas. A super-influential philosopher, Immanuel Kant, said that space is something that exists in our minds, and we each have the same unique "space" in our minds. And it turns out that, for Kant, this space had to be Euclidean. To argue that we can come to know complex truths about non-material things,...
The art and architecture of the early modern period also reflect the Euclidean idea of space. Here's the first important perspective painting of the Renaissance: the Trinity by Masaccio. Now we are used to two-dimensional pictures that look three-dimensional because we have photography and television and iPhones and so on. In the Renaissance, they ...
This article is based on Grabiner's talk at the Ada Lovelace Symposium, which took place in December 2015 at the University of Oxford. Here's a video of the talk: Judith V. Grabiner, Flora Sanborn Pitzer Professor of Mathematics at Pitzer College, is the authorof three books and many articles (most recently The Role of Mathematics in Liberal ArtsEd...
In 1557, Robert Recorde invented the equals sign, written with two parallel lines (=), because “noe 2 thynges, can be moare equalle”. “2 + 3 = 5” is much easier to read. Unfortuantely, the meaning of “equals” changes with the context — just ask programmers who have to distinguish =, == and ===.
The list below has some of the most common symbols in mathematics. However, these symbols can have other meanings in different contexts other than math.
Sep 6, 2024 · Euclidean geometry is the study of plane and solid figures on the basis of axioms and theorems employed by the ancient Greek mathematician Euclid. The term refers to the plane and solid geometry commonly taught in secondary school. Euclidean geometry is the most typical expression of general mathematical thinking.
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