Leonardo Pisano, Fibonacci, Leonardo Bigollo, 1175-1250, Middle AgesItalyMathematician, the first research in the WestFibonacci numberAnd put modern writing numbers andmultiplierBit value ofRepresentationThe system is introduced into Europe.His work written in 1202《Book of Calculations》It contains many GreekEgypt、arabMathematics in India and even in China.[1]
Leonardo's father was named Guilielmo (William), nicknamed Bonacci (meaning "good, natural" or "simple").William is a businessmanNorth AfricaBelt and Road Work (TodayAlgeriaBejaia），At that time, young Leonardo had already started to help his father, and he learnedArabic numerals。
study
Sensible useArabic numeralsthanRoman numeralsMore effective, Leonardo tomediterranean seaHe learned from the famous Arab mathematicians at that time and returned to China in about 1200.In 1202, at the age of 27, he wrote what he learned into《Book of Calculations》（Liber Abaci）。This book shows the newdigital systemPractical value.This book greatly influenced European ideas, but before the invention of printing after the third century,decimal systemNumbers are not popular.(Example: Ptolemaeus in 1482World map, printed by Lienhart Holle in Ulm)
achievement
Leonardo once became a math and science loverFriedrich II (an emperor of the Holy Roman Empire).
European mathematicsGreek After the decline of the Ming Dynasty, it was in a state of stagnation for a long time, and there was no sign of recovery until the 12th century.This recovery was initially stimulated by the translation and dissemination of Greek and Arab works.The exploration and discussion of the achievements of classical mathematics in Greece and the East eventually led toThe RenaissanceDuring the 15th and 16th centuries, European mathematics was on the upsurge.Renaissance outpost Italy, due to its specialgeographical positionIt has become the melting pot of Eastern and Western cultures through its trade links.Italian scholars began translating and introducing Greece andarabMath literature.
In Europe,Dark AgeFibonacci, the first influential mathematician since then (about 1175-1250), whose representative Latin works Liber Abaci and Practice Geometry are also based onarabicCompiled with Greek materials, Fibonacci, also known as Leonardo of Pisa, followed his father to learn arithmetic from Arabs in North Africa in his early years, and later traveled to countries along the Mediterranean coast. After returning to Italy, he wrote the Book of Computing (Liber Abaci, 1202, also translated as the Abacus Sutra).The greatest merit of the Book of Computing is its systematic introduction to IndiaNumeration, influenced and changed the appearance of European mathematics.It is said that the Suanjing was written in 1228Revision, in which the famous“Fibonacci sequence”。Practice Geometry (1220) focuses on Greek geometry and trigonometry.
Fibonacci's other mathematical works include《Square numberLiber Quadratorum (1225), Flos (1225), etc., the former specializes in the quadratic Diophantine equation, and the latter mostly refers to the court of Frederick IIMathematical contestQuestion, which contains aCubic equation/10 2x2 10 x ～ - 20, Fibonacci demonstrated that its root cannot be made with a ruler (that is, it cannot beEuclidHe also gave the approximate solution of the equation without explanation (J-1.36880810785).
The foundation of calculus andanalytic geometryThe invention ofModern mathematicsThe rise of.The ideological roots of calculus (especiallyIntegral calculus）It can be traced back toAncient Greece, Chinese and Indian works.Before Newton and Leibniz finally formulated calculus, it had gone through nearly a century of gestation.In this gestation periodCalculusPioneers with direct contributions include KeplerKavalieri, Fermat, DescartesWallisBarrow (1630-1677) and other mathematicians.
In general,rabbitAfter two months of birth, Zizi has the ability to reproduce. A pair of rabbits can produce a pair of rabbits every month.If all rabbits are immortal, how many pairs of rabbits can be bred in one year?
Let's take a pair of newly born rabbits and analyze them:
In the first month, the rabbits have no reproductive capacity, so they are still a pair;
Two months later, there were two pairs of rabbits in total;
Three months later, the old rabbit gave birth to another pair. Because the little rabbit had no reproductive capacity, there were three pairs in total;
……
The following table can be listed by analogy:
Months passed
zero
one
two
three
four
five
six
seven
eight
nine
ten
eleven
twelve
Population logarithm
zero
one
one
two
three
five
eight
thirteen
twenty-one
thirty-four
fifty-five
eighty-nine
one hundred and forty-four
Rabbit problem
The numbers 1, 1, 2, 3, 5, 8 - - in the table form a sequence.This sequence has a very obvious feature: the sum of the two adjacent items in front constitutes the latter item.This sequence isItalyMedieval mathematician Fibonacci《Book of Calculations》Of this seriesGeneral formulaIn addition to having the property of an+2=an+an+1, we can also prove that the general formula is: an=1/√ 5 [(1/2+√ 5/2) ^ n - (1/2 - √ 5/2) ^ n] (n=1,2,3.....) (√ 5 meansRadical5）。
In this general formula, although all an arepositive integerBut they are expressed by some irrational numbers.
That is, in the higher sequence, two consecutive“Fibonacci number”The sequences ofGolden ratio(1.618:1 or 1:0.618).
1. For any item in Fibonacci seriesSquare numberAre equal to the product of the two adjacent terms plus or minus 1;
2. Any of the four adjacentFibonacci number, the product of the middle two numbers（inner product）Product of two numbers on both sides（Outer product）The difference is 1.
