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Posted at: 2019-07-15 16:05:17

René Descartes was a French mathematician lived around the early 17th century. He was more of the philosopher than a mathematician, but his same philosophical nature led a huge foundational step into mathematics, from cartesian system to analytical geometry. Leibniz was one of few mathematicians influenced by him.
Descartes Theorem is one of legacy work left by him with us.
It states or gives us a quadratic equation that is followed or need to satisfied by the 4 kissing circles, or mathematically 4 mutually tangent circles. (k1+k2+k3+k4)^2 = 2((k1)^2 + (k2)^2 + (k3)^2 + (k4)^2)
Here k = 1/r is defined as the curvature of a circle.
The curvature of the circle(k) signifies an amount or rate of change in direction as you move along the circumference of a circle.
Given three mutually kissing circles(to each other), mutually tangent circles, with Descartes Theorem we can determine the radius of 4th circle.
There exists 2 solution, or two circle that satisfies condition, the sign identifies circle uniquely.
If it is negative, then the radius obtain is of larger circle which circumscribes all three circle, else radius is of smaller circle inscribed between all three kissing circles.
#descartes #maths
#cartesian #theorem #geometry #ilovemaths #mathfacts #circles #kissingcircles #geometryclub #geometrycollection #collection #mathcollection #mathproblem #mathful #mathlife #mathmeme #philosophy #french #legacy #europe #leibniz #analysis #mathhelp #maths163 #mathematician #ru

Likes: 54

Posted at: 2019-07-08 04:59:21

Srinivasa Ramanujan [FRS] was the Indian Mathematician. He is considered to be one of the greatest mathematicians lived on Indian soil. Despite any formal training in mathematics, he was able to understand and practice maths by just mere reading and playing with numbers.
He loved the maths so much that he practice it till death bed... Ramanujan's Constant is one of the most interesting constants in the world of mathematics.
Ramanujan Prime is the prime number satisfies the condition stated by him, "Rn is a smallest positive integer such that for n >= 1 and for all x >= Rn satisfies condition ' π(x)-π(x/2) >= n '. "
Rn = [2, 11, 17, 29, 41, ...] Rn is necessarily a prime number or a prime by minimality means
π(Rn) - π((Rn)/2) = n ..... (the minimality condition)
It is so since the function π(Rn) is a step function, increases by atmost 1. The resultant function π(Rn) - π((Rn)/2) is a step function, increases by one or zero.
As n tends to infinity, there exist asymptotic equation Rn ~ p_2n this can easily observe since 46 % of a prime number less than 19000 are Ramanujan Prime (Rn)
And there exist many more, some are known and some unknown which you can research.
#Ramanujan #ramanujanprime #SrinivasRamanujan #ramanujanconstant #mathsconstant #constants #integer #e #pi #epi #hardy #ramanujanswork #ramanujanlostnotebooks #lostnotebook #incredible #beautiful #beautifulEquations #ilovemaths #mathful #math #mathproblem #mathfacts #mathmeme
#maths163
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#mathematician
#ru

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Posted at: 2019-06-28 14:44:15

Leonhard Euler was the Swiss mathematician. He is considered to be one of the greatest mathematicians ever lived. He was taught by Johann Bernoulli in the early days. His great contribution includes in fields of number theory, graphs, infinite series etc. despite of being one eye blind most of life and fully blind in his late days, he worked and scratch the surface of almost everything in mathematics.
All knowledge is from logic we make.
Logic is the foundation of all the knowledge we acquire
One of his work, Euler Theorem also sometimes referred as Euler-Fermat Theorem, it states a weird exponential relationship between two numbers in modulo arithmetic. Fermat Little theorem is special case of Euler theorem, where n considered here is prime.
Theorem states that, given a positive integer a, n with the relationship of primeness, relatively prime, i.e. gcd(a, n) =1
a^(phi(n)) = 1 mod n
Here = refers congruence symbol
phi(n) is Euler Totient function, another one of important function in number theory.
phi(n) is defined as the count of a number less than n relatively prime to n
#LeonhardEuler
#euler
#EulerQuotes #LeonhardEulerQuotes #BeautifulEquations #amazing #mathproblem #fascinatingEquation #mathsConstants #mathmeme #mathlife #mathful #WowEquation
#Logic #knowledge
#mathematician #numbertheory #mathfact #mathtip
#maths #mathematics
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#ilovemaths #maths163
#ru

Likes: 19

Posted at: 2019-06-26 12:37:16

Jacob Bernoulli was a Swiss mathematician and from well family of Bernoulli. He was greatly influenced by Leibniz. He leads founding stones for the calculus of variations. He derived the law of large number, great work in the field of probability. He also found that sum of series of 1/ n diverges.
Another main part of is works involved discovery of mathematical constant 'e' as solution compounding interested problem, smaller there compound period more you earn at year end.
With all these, he is also credited for Binomial Distribution with come with Bernoulli trials. Here there are pretty good assumptions considered,
1. All events considered are independently and mutually exclusive
2. Kind of binomial trail means dealing with only two possible outcomes, success and failures
3. Probability of respective event(success or failure) remains constant throughout the trial.
The literal definition of Bernoulli Trial can be stated as, "Independent repeated trials of an experiment with exactly two mutually exclusive possible outcomes are called Bernoulli Trials"
Here variables used
p --- probability of success
q --- probability of failures
n --- numbers of trials
Other are self-explanatory
#bernoulli #jacobbernoulli #swiss #ilovemaths #e #trial #compoundinginterest #onedollar #mathslogic #logic #mathsconcept #bernoullitrial #mathsproblem #math #mathmeme #money #moneymaths #mathslovers #mathful #mathsnight #numbers #probability #calculus #mathematics #maths163 #mathematician #ru

Likes: 37

Posted at: 2019-06-20 18:35:19

Bhaskara II was an Indian mathematician, lived around 12th century AD. He is considered among the greatest mathematician of medieval India. He was born in Bijapur in Karnataka.
His main work includes a treatise on Siddhānta Shiromani, which is a combination of four works , Lilāvatī, Bījagaṇita, Grahagaṇita and Golādhyāya. He is considered to serve as head of an astronomical observatory of Ujjain.
In Bījagaṇita section he come out with chakravala method, which is many time credited to Jaydev, who lived a century before Bhaskara, but it can debated. But there in between chakravala method, he mentioned identity named after him as Bhaskara Indentity/Lemma which states
For equation Nx^2+k=y^2 implies
N((mx +y)/k)^2+(m^2 -N)/k = ((Ny+mx)/k)^2
#bhaskara #algebra #mathidentity #mathlemma #ilovemath #indianmath #india #mathproblem #mathfact #mathfun #mathtutorial #mathgame #mathtip #mathway #pellquatition #equation #astronomer #observatory #usa #mathmeme #mathmystery #formula #mathwork #americaindia #bijganita #mathematica #mathematician #math #maths163

Likes: 21

Posted at: 2019-06-17 16:12:19

Carl Friedrich Gauss was the German Mathematician is known for his significant contribution in many fields of pure mathematics, all modulo convection for writing we used was first observed in his book Disquisitiones Arithmeticae, it explain all things necessary to start learning number theory. His work in mathematics include gaussian distribution, guassian filter, etc. One of his base line which he established lead to development in Fast Fourier Transfrom.
He was also great physicist , he did great work in magnetism. He is also known as Prince of mathematics
He was a philosophical guy, one of many of saying is "The enchanting charms of this sublime science reveal only those who have the courage to go deeply into it"
#CarlFriedrichGauss, #Gauss #gaussquotes #Gaussian #prince #princequotes #mathsnote #mathway #new #way #modulo #probability #physics #physicsquotes
#knowledge #mathsquotes #ilovemaths #mathfacts #mathproblem #mathful #mathlover #mathit #ganit #mathematics #learning #enjoyment
#mathematician #maths163
#ru

Likes: 31

Posted at: 2019-06-16 12:17:02

John Wilson[FRS] was an English mathematician, lived around the late 18th century. He was a student of well-known mathematician Edward Waring. He received Fellowship of Royal Society in 1782. The two things named after him in mathematics are Wilson Prime and the Wilson Theorem.
Wilson Theorem
It states that if any number p is prime then it must statisfies the condition given below
(p-1)! = -1 mod p
Here I use = for congruence symbol
The above is both sufficient and necessary condition to be a number prime unlike that of Fermat Little primality test.
Though it is very computationally infeasible to work out this test on large n, worst performance than trial division, but its art work, artwork in mathematics
And number theory develops without thought of feasibility. So come on mathematicians lets work on numbers.
#wilson #wilsontheorem #johnwilson #waring #primality #primenumber
#mathproblem #prime #wilsonprime #ilovemaths #mathful #mathfacts #mathlover #mathsnotes #weekend #mathematical #englishmath #british #usa #mathmeme #mathnight #ganit #mathit #mathematician #mathematics #maths163 #ru

Likes: 35

Posted at: 2019-06-11 10:22:22

Jacob Bernoulli was a Swiss mathematician and from well family of Bernoulli. He was greatly influenced by Leibniz. He leads founding stones for the calculus of variations. He derived the law of large number, great work in the field of probability. He also found that sum of series of 1/ n diverges.
Another main part of is works involved discovery of mathematical constant 'e' as solution compounding interested problem, smaller there compound period more you earn at year end.
With the rule, if $1 is compounded on n intervals in a year and then 1/n would be the rate of interest, continuous compounding yield $e at year end
#bernoulli #jacobbernoulli #swiss #ilovemaths #e #econstant #compoundinginterest #1dollar #mathslogic #logic #mathsconcept #mathsproblem #math #mathmeme #money #moneymaths #mathslovers #mathful #mathsnight #numbers #constants #calculus #mathematics #maths163 #mathematician #ru

Likes: 64

Posted at: 2019-06-06 08:13:09

Blaise Pascal was a French mathematician, physicist, inventor. He is popularly know due to Pascal triangle which gives binomial coefficient in binomial expansion and also due to physics work on fluids.
He popularized the triangle made with rule , starting with 1, and each next row formed with 1 at edges and adding previous 2 elements exactly above in previous row, triangle formed is known by as Pascal's Triangle and rule is known as Pascal Identity or Pascal rule. (N-1) C (k-1) + (N-1) C k = n C k
#BlaisePascal
#Pascal, #PascalTriangle #mathslovers #mathsend #mathsmemes #triangle #mathspuzzle #french #combinatorics #combine #number #numberfacts #binomial #statisticsclass #factorial #fibonacci #mathsconcepts #mathtriangle #mathsmylife #europeanmaths#ilovemaths #maths163 #mathematics
#mathematician
#ru

Likes: 39

Posted at: 2019-06-02 07:05:05

Apollonius of Perga was a Greek mathematician. His work included mainly in geometry, and astronomy. Also he is remember for his work in conic section, there he describe how circle, ellipse, parabola, and hyperbola. Most of work of his is lost now, but still we have significant remained which tell about his legacy.
In geometry of triangles , there is important theorem known as Apollonius Theorem. It is about median relationships with sides of triangle.
In any triangle sum of square of any two sides of any triangle equals twice of square of half of third side added with twice the square of median on third side.
In traingle BAC , and BE is median
Then
AB^2 + BC^2 = 2(BC/2)^2 + BE^2
#apollonius #physics #conics #science #greek #geometry #astronomy #astronomer #geometer #scientist #insta #ancientmath #triangle #square #pythagoras #maths #ilovemaths #mathmylife #mathspuzzle #mathsfacts #perga #science #mathsformula #mathematics #maths163
#mathematician #ru

Likes: 42

Posted at: 2019-05-29 05:15:51

Sir Isaac Newton [FRS] was an English mathematician, physicist , astronomer. He revolutionarized the every aspect of astronomy, physics and mathematics by developing calculus, systematic approach to solve equations. I'm physics is know for the famous three laws of motion, and Law of gravition.
Even before he reach full development of calculas he discovered various techniques for numerical approximation. Newton Method, or well known Newton - Raphson Method approximates the root of differentiable function. It converges quadratically, approximation terms double on each iteration.
#newton #calculus #ilovemaths #mathsconcepts #isaacnewton #maths #mathspuzzle #newtonmethod #History #HistoryFacts #education #science #numerical #mathmemes #mathriddles #mathsfacts #formula #mathmethods
#imaths #mathsisfun #mathskills #mathtest #astronomer #beautifulmath #beautiful #mathteaser #mathematics #Mathematician #maths163 #ru

Likes: 25

Posted at: 2019-05-28 16:11:26

Alan Turing was a English mathematician whose efforts cracked the enigma code, and gave mordern day so called computer.
Turning Machine is basis of modern computers, any problem that can't solved by Turing Machine can't solve by any computer in world.
#AlanTuring
#AlanTuringQuotes
#theEnigma
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#TuringMachine #ComputerScientist #OnComputableNumbers #Cryptanalyst #Computers #Computing #CodeBreaker #BletchleyPark #WorldWar2 #Homosexuality #Pardoned #AlanTuringLaw
#mathematician
#maths163 #mathsquotes #ilovemaths
#ru

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