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2. Fraction - Wikipedia

   en.wikipedia.org/wiki/Fraction

   (For example, two-fifths is the fraction ⁠ 2 / 5 ⁠ and two fifths is the same fraction understood as 2 instances of ⁠ 1 / 5 ⁠.) Fractions should always be hyphenated when used as adjectives. Alternatively, a fraction may be described by reading it out as the numerator over the denominator, with the denominator expressed as a cardinal ...

3. Continued fraction - Wikipedia

   en.wikipedia.org/wiki/Continued_fraction

   Continued fractions can also be applied to problems in number theory, and are especially useful in the study of Diophantine equations. In the late eighteenth century Lagrange used continued fractions to construct the general solution of Pell's equation, thus answering a question that had fascinated mathematicians for more than a thousand years. [9]

4. Euler's continued fraction formula - Wikipedia

   en.wikipedia.org/wiki/Euler's_continued_fraction...

   Euler derived the formula as connecting a finite sum of products with a finite continued fraction. (+ (+ (+))) = + + + + = + + + +The identity is easily established by induction on n, and is therefore applicable in the limit: if the expression on the left is extended to represent a convergent infinite series, the expression on the right can also be extended to represent a convergent infinite ...

5. Expression (mathematics) - Wikipedia

   en.wikipedia.org/wiki/Expression_(mathematics)

   A formal expression is a kind of string of symbols, created by the same production rules as standard expressions, however, they are used without regard to the meaning of the expression. In this way, two formal expressions are considered equal only if they are syntactically equal, that is, if they are the exact same expression.

6. cis (mathematics) - Wikipedia

   en.wikipedia.org/wiki/Cis_(mathematics)

   The cis notation is convenient for math students whose knowledge of trigonometry and complex numbers permit this notation, but whose conceptual understanding does not yet permit the notation e ix. The usual proof that cis x = e ix requires calculus , which the student may not have studied before encountering the expression cos x + i sin x .

7. Solving quadratic equations with continued fractions - Wikipedia

   en.wikipedia.org/wiki/Solving_quadratic...

   If this infinite continued fraction converges at all, it must converge to one of the roots of the monic polynomial x 2 + bx + c = 0. Unfortunately, this particular continued fraction does not converge to a finite number in every case. We can easily see that this is so by considering the quadratic formula and a monic polynomial with real ...

8. Calculator input methods - Wikipedia

   en.wikipedia.org/wiki/Calculator_input_methods

   Calculators that use infix notation tend to incorporate a dot-matrix display to display the expression being entered, frequently accompanied by a seven-segment display for the result of the expression. Because the expression is not evaluated until it is fully entered, there is provision for editing the entered expression at any point prior to ...

9. Egyptian fraction - Wikipedia

   en.wikipedia.org/wiki/Egyptian_fraction

   The Rhind Mathematical Papyrus. An Egyptian fraction is a finite sum of distinct unit fractions, such as + +. That is, each fraction in the expression has a numerator equal to 1 and a denominator that is a positive integer, and all the denominators differ from each other.