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A continued fraction is an expression of the form = + + + + + where the a n (n > 0) are the partial numerators, the b n are the partial denominators, and the leading term b 0 is called the integer part of the continued fraction.
That expression is called the continued fraction representation of 415 / 93 . This can be represented by the abbreviated notation 415 / 93 = [4; 2, 6, 7]. (It is customary to replace only the first comma by a semicolon to indicate that the preceding number is the whole part.)
Periodic continued fractions are in one-to-one correspondence with the real quadratic irrationals. The correspondence is explicitly provided by Minkowski's question-mark function. That article also reviews tools that make it easy to work with such continued fractions. Consider first the purely periodic part
The following list includes the continued fractions of some constants and is sorted by their representations. Continued fractions with more than 20 known terms have been truncated, with an ellipsis to show that they continue. Rational numbers have two continued fractions; the version in this list is the shorter one.
In mathematics, regular continued fractions play an important role in representing real numbers, and have a rich general theory touching on a variety of topics in number theory. Moreover, generalized continued fractions have important and interesting applications in complex analysis .
NAD+ supplements, IV drips, and injections have gained a lot of traction on social media due to their supposed anti-aging benefits. Here, doctors reveals the truth behind the trend.
The square root of 5 can be expressed as the simple continued fraction [;,,,,, …] = + + + + +. (sequence A040002 in the OEIS)The successive partial evaluations of the continued fraction, which are called its convergents, approach :
Nvidia (NASDAQ: NVDA) and other AI stocks plunged on Monday, Jan. 27, as investors responded to the threat from DeepSeek, the Chinese AI chatbot that rivals top models like ChatGPT for a fraction ...