Math

[Cyber2_O.o 64]

Okay, I feel like I'm intruding onto this very deep discussion on math, but I personally think that math is awesome. (Although my mind might change once I see all of that senior math you guys have to do.)

Then again, the Magnum is a mathematical turret, and I don't like it, so I guess there are some parts in math I don't really like.   

[Adab 2,896]

Okay, I feel like I'm intruding onto this very deep discussion on math, but I personally think that math is awesome. (Although my mind might change once I see all of that senior math you guys have to do.)

Then again, the Magnum is a mathematical turret, and I don't like it, so I guess there are some parts in math I don't really like.   

You're not intruding or causing any disturbance, this Topic is to Discuss & Share your opinions related to Maths, so feel free to! ;)

[girl_from_kurdistanX 383]

Golden Ratio

The golden ratio, or the number 1.618, is one of the beauty of the math world that can be traced from the corners of this great world from human body organs to outstanding artistic and architectural artworks around the world and even the development of sunflower seeds.also in art:

The golden number or golden ratio of 1.618 is the result of the efforts of scientists such as Euclid, Lukapacilly, Leonard Fibonacci. The researchers believe that the most beautiful surfaces and shapes are those that have a golden ratio. The objects  made with this ratio have a special symmetry and beauty that appear to be very beautiful for the human eye.

The golden number is usually represented by the Greek "Phi" and is shown as follows

Different fields of a golden ratio:

1-If in a segment, the ratio of the larger to the smaller is equal to the ratio of the whole line to the large part, this ratio is definitely a golden value of 1.618.

2-Another area where you find the golden ratio is the Fibonacci sequence. In this sequence, which is 1, 1, 2, 3, 5, 8, 13, 21, ... If we consider the numbers after 2 and divide each of them into our pre-number, we see very close numbers We will have the golden ratio of 1.618. The more you split up, the closer you get to the golden ratio.

How to draw golden rectangle and golden spiral or Fibonacci:

To draw a golden helix or Fibonacci, we draw a bow from the vertex (corner) of each square to the side of that square. The spiral is also called a logarithmic spiral.bow lentgh = squre side lengths.

The golden ratio is in many structures

The spiral of the human ear, the snail, the spiral structure of the galaxies and all the beauties of nature, including the leaves of the trees, the lines and the role on the feathers of the peacock and the sunflower spirals, have been met.

This number is also very useful in the human body. The beauty of the face, the beauty of laughter, fitness and cheerfulness are all from the king of divine works in the creation of mankind. If you look at the history of the golden number, you see Leonardo da Vinci the first to measure the exact proportion of human bones and prove that this is a ratio of a golden number.

In your fitness assessment, you can divide the toe-to- belly button distance over the  belly button to the top of the head, and compare the result with a number of 1,618. The closer you get to the 1.618, it means you have a good fitness.

[girl_from_kurdistanX 383]

riddle time

The three houses are separated by a large farm. 

The farm has three door for entrance. 

We clearly identified the position of the doors and the houses in the form below. 

Each of the doors belongs to one of the houses, and the inhabitants of each of the houses have to go through a special way and travel on their own.

Can you draw three ways from the entrance to the houses so that they do not cut each other? 

Indeed, it should be said that the door in middle belongs to a middle house, but the door on the right belongs for the house on the left and left door is for right house. 

How do you draw these three ways ???

answer:

Edited July 1, 2019 by girl_from_kurdistanX

[Guest]

Okay, I feel like I'm intruding onto this very deep discussion on math, but I personally think that math is awesome. (Although my mind might change once I see all of that senior math you guys have to do.)

Then again, the Magnum is a mathematical turret, and I don't like it, so I guess there are some parts in math I don't really like.   

Welcome here! I certainly hope that a few math questions don't change your love for Math! 

[girl_from_kurdistanX 383]

Fields Medal

The coin is made of gold, with the image of Archimedes.

Fields Medal, officially known as International Medal for Outstanding Discoveries in Mathematics, award granted to between two and four mathematicians for outstanding or seminal research. The Fields Medal is often referred to as the mathematical equivalent of the Nobel Prize, but it is granted only every four years and is given, by tradition, to mathematicians under the age of 40, rather than to more senior scholars.

The Fields Medal is regarded as one of the highest honors a mathematician can receive, and has been described as the mathematician's Nobel Prize.

The name of the award is in honour of Canadian mathematician John Charles Fields.

The medal was first awarded in 1936 and it has been awarded every four years since 1950.

This prize is called "Nobel Prize in Mathematics"

Nobel Prize is not given in the field of mathematics.There is no Nobel Prize for mathematics.

An important point about this award is that the prize is awarded only to people under the age of forty who have discovered an important mathematical discovery.

This award is one of the most prestigious scientific awards.

Only 60 people received this award.The last time was held in 2018.

First Woman To Win Fields Medal 

1977–2017 

In 2014, the Iranian mathematician Maryam Mirzakhani became the first female Fields Medalist.

Maryam Mirzakhani, the first and only woman to win the prestigious Fields Medal.

[Sacrifice 2,278]

This topic is an effective step in improving grades of no-lifers in TO, so they can concentrate on studies, side by side, with their game. However bro if you can also make a "Biology" club, that is because I am not a math student anymore. Lol from where I am we drop math after 10th if we want. But we have to study Bio in-compensation  :D

[Guest]

This topic is an effective step in improving grades of no-lifers in TO, so they can concentrate on studies, side by side, with their game. However bro if you can also make a "Biology" club, that is because I am not a math student anymore. Lol from where I am we drop math after 10th if we want. But we have to study Bio in-compensation  :D

Thanks! Well anybody at all is welcome here! I would be happy to make a biology club but to be quite honest the most I know about Biology is Photosynthesis (I get utterly lost in Biology).

[Sacrifice 2,278]

Thanks! Well anybody at all is welcome here! I would be happy to make a biology club but to be quite honest the most I know about Biology is Photosynthesis (I get utterly lost in Biology).

I don't even know that bit. Krebs cycle, ETC ughhh. 

[girl_from_kurdistanX 383]

Möbius strip

(Mobius or Moebius)

Mathematics is full of wonder.

The Mobius strip is a strip that has two edges to put together and creates a loop. Of course, the edge of the end must be rotated halfway before connecting to the other edge. You can draw a continuous line between the two points of the strip without cutting off its edge. Therefore, the Mobius strip has only one surface and only one border (edge). 

Mobius has an interesting feature that reverses the relationship between "inside" and "out". That is, every point of a mobiosis level while inside it is also out!

Moebius, is a surface with only one side

The mobius tape is a property that reverses the relationship between the inside and the outside, that is, every point of a mobiosis surface while inside it out. And there is a kind of transformation in the nature of a space. In fact, space finds a dual but continuous property. .

A half-twist clockwise gives an embedding of the Möbius strip different from that of a half-twist counterclockwise.

This tape was independently discovered and recorded by two German mathematicians Augustus Ferdinand Mobius and John Benedict in 1858.

Interesting Tips on the Mobius Bar:

If we draw a line on the Mobius tape along the and continue it, then the line returns to the starting point and the two sides of the strip line are Joining eachother.

The Mobius strip has other unexpected properties, for example, when we try to strip this strip along its length, we get a taller bar with two turns instead of having two stripes.

Also, by repeating this again, there are two twisted mobius strips. By continuing this, the strip is cut off sequentially and the unexpected images are created at the end of the work, known as paradromic rings. Also, if we remove this tape from one third of the width of the strip, in this case we obtain two interleaved mobis strips of different lengths.

Mobius tape can be a special kind of Klein bottle.

The Mubius bar can in some way be considered as a symbol of cultural duality interaction.

The Mobius Bar for many artists also has its own attraction and has been given special attention in their works. The figure below is a famous Polish designer, Adam Pekkalski (Adam Pekalski)

In this plan, Palksky portrays a regular forest, and a forest man is located in the center of the forest lines. Slightly higher, we see a rabbit fleeing from a wolf. In fact, the rabbit escapes from the inside of the mobius path, and the hungry wolf moves from the inside out! In this way, the special feature of the Mobius strip is depicted.

[girl_from_kurdistanX 383]

riddle time

 

answer:

 

 

Missing Sunday:

6713

The first digit from the left shows the number of characters for the day. (For sunday is 6)

The next digits show the day of the week (note that the week starts from monday)

The next two digits are the sum of the two digits obtained (the first two digits).

Edited July 5, 2019 by girl_from_kurdistanX

[Guest]

 

riddle time

 

answer:

 

 

 

 

Just a guess but is it 9711?

On a separate note, may I ask if traffic merging is an example of a vector field?

 

What I'm trying to learn has absolutely blown my mind at the simplest levels.

[Guest]

On a separate note, may I ask if traffic merging is an example of a vector field?

Maybe?

 

In a vector field, every vector is defined as a function of a point. So if every car's direction of motion and speed is a function of its position, yes. That is, if a car's position is (x, y) on the xy plane, its velocity vector would be <f(x), g(y)>, where f and g are some functions. However traffic merging would be a rather atypical example of a vector field, since although in traffic a car's velocity sometimes depends on its position, it rarely depends solely on its position, and hardly ever is the relationship between a car's position and velocity the same for every single car in question.

Edited July 2, 2019 by ThirdOnion

[Person_Random 4,991]

this just changed so much over this weekend/.

[girl_from_kurdistanX 383]

Rubik's Cube

Rubik's cube is the best selling puzzle toy in history.

Rubik's cube, 40 years after its birthday, is fun yet.

The "magic cube" was invented in 1974 by Hungarian architectural professor Erno Rubik. After re-launching the market under the rubik's cube, more than 350 million sold out of this toy around the world.

In the mid-1970s, Erno Rubik worked at the Department of Interior Design at the Academy of Applied Arts and Crafts in Budapest. Although it is widely reported that the Cube was built as a teaching tool to help his students understand 3D objects, his actual purpose was solving the structural problem of moving the parts independently without the entire mechanism falling apart. He did not realise that he had created a puzzle until the first time he scrambled his new Cube and then tried to restore it.

For the first time, Ernou Rubik found a solution to the cube until the English mathematician David Sinester wrote the first book to solve Rubik's cube, in which he wrote Rubik's connection with a branch of mathematics (group theory), and he first called the magic cube The Rubik's Cubewas introduced and since then Rubik's name has become customary.

David Jooner also wrote Merlin's Rubik's book. In this book, he examined the permutations and the relation between Rubik's and mathematical branches, Jouiner's book was a start for other mathematicians and enthusiasts to write their own findings about the cube. In the case of finding an algorithm that can solve a cube in the least number of moves, in 2006, the first two algorithms of 26 motion were written by two mathematicians, one year later by the same two people, the number dropped to 25, compared to 2010 forever The puzzle was solved and it was definitely proved that the upper limit of the number of moves to solve the Rubik's cube is 20 . Of course, while Tim Wong was able to overthrow the hypothesis in 2015 by solving a cube with 19 moves.

this is why 20 is god's number in Rubik's Cube.

But the speed solution of the cube was developed and completed by professional cubers.

Rubik's Color:

The Rubik's Cube is a mechanical puzzle that has 26 small cubes that are joined by a mechanism and enables the cube to rotate in all its faces.

In the classic color scheme, Rubik colors are (yellow to white, blue against green and orange to red).

In Japanese color (blue to white).

In the American color, they use black instead of white.

some famous method for solving rubik's cube:

Corners-first method(Ortega's method):

In this method, first, the corners of the cube are arranged, then the edge cubes are placed in place. In the first Rubik's cube tournament, most of the participants use this technique and the first person to win was the Thai mines a thailand refugee from the United States who solved the cube in this method In 22.95 seconds. This method is less used today.

This is also called Ortega's method.

this is Minh Thai 

Fridrich method:

The most popular Speedsolving method is the CFOP (Cross, First 2 layers, Orientation of last layer, Permutation of last layer) a.k.a Fridrich Method. Unlike The beginner's method, the Speedsolving method focuses mainly about solving the Rubik's cube in the fastest and most efficient way, rather than the easiest way. 

This method was originally developed by Dr. Jessica Friedrich in 1981, when she was a student at that time, and she was only 17 years old. she took part in the first World Rubikon in 1982 but did not get a position (she reached the tenth). she did her own way Developed and posted on her own website on the Internet. her technique was accepted by professionals, so in the second tournament in Toronto in 2003, Friedrich's method was the method most used by the contestant. In this tournament, Den Knight (1) (with an average of 20 seconds) and Jessica get second place (with an average of 20.48 seconds). her best record in this tournament was(17.12 seconds).Jessica had personally taught the correct solution to Den Knight, the first person in the tournament !!!

Friedrich's method consists of four parts: a) making the cross at a low level;  placing the four corners with the middle edge (F2L); c) rotating all the upper cubes so that the upper parts of the surface are all one-colored (OLL) (Orientation of Last Layer (d) Movement of high level parts in its place and completion of the cube (PLL) (Permutation of Last Layer)

Friedrich's method was complemented by other professionals, including the method (ZBF2L, COLL, ...), which were very effective in reducing time.

nowadays most famous cubers use this method.

Petrus method:

This technique was developed by Lars Peters, a participant in the first World Championships. In the method of Peters, we make a 2 * 2 * 2 cube first in the corner, then turn it into a 2 * 2 * 3 block without breaking the cube, then place the edges of the opposite surface and arrange the corners. This arranges two rows of cubes, followed by the Jessica method, with the difference that we first align the edges and then the upper corners.

Lars Peters in the first Rubik's tournament managed to cube his way in 30 seconds. Professional cubers often use the Lars Peters method for the least number of moves (FMCs) in the Rubik's tournaments (in the item tournament there is the least number of moves that will solve the cubes in that cube in the lowest number of moves.) The record for this item There are currently 19 moves.

Roux method:

In this method, first, a 1 * 2 * 3 block on the left side and one block on the opposite side (right) at the bottom of the cube. Then create the remaining 4 corners, then place the 6 edges and the centers in place. we give. The average solution of the cube was recorded with this method for 15 seconds.

ZZ method:

This method, which is the newest method of speed, was invented by Zbigniew Zubrówski in 2006. The method is highly professional and based on the algorithm (the number of high-level algorithms is 177 algorithms and the number of moves to complete the cube is very low) so that it can not be expressed in simple language.

we have 43,252,003,274,489,856,000 Composition of different states of a Rubik's Cube. It's interesting to note that no matter how the cube is arranged, it can be solved with 20 moves or even less.

true story:

Graham Parker, a construction worker in Hampshire, was able to solve it in 2009 and after 26 years of effort. He cried after the victory. 

Graham, 45, from Portchester, Hants, has been tirelessly trying to solve the riddle of the Cube since he bought the toy in 1983. Graham has endured endless sleepless nights and after more than 27,400 hours he finally managed to conquer his personal Everest.

Builder Graham said: "I cannot tell you what a relief it was to finally solve it. It has driven me mad over the years - it felt like it had taken over my life.

"I have missed important events to stay in and solve it and I would lay awake at night thinking about it."

"Friends have offered to solve it for me and I know that you can find solutions on the web but I just had to do it myself."

world records:

human:

Feliks completed the world-famous puzzle in just 4.22 seconds to take the title from SeungBeom Cho (Republic of Korea) who, according to the World Cube Association (the official organisation that regulates Rubik's Cube competitions), held the record with a time of 4.59 sec.

robot:

0.38 Second Rubik's Cube Solve

There have been 350 million Rubik's cubes sold. We will estimate that 50% of the people who have these cubes can solve them. That leaves us with ~180 million people who can solve the Rubik's Cube. That means around 3% of the total world population can solve the Rubik's Cube.

 

how to solve rubik's cube?

i offer use this site:

https://ruwix.com/

Edited July 5, 2019 by girl_from_kurdistanX

[girl_from_kurdistanX 383]

@LOLKILLERTOTHEDEATH thx for adding me in math club.i appreciate it. :)

[girl_from_kurdistanX 383]

unsolved problem in math

twin prime conjecture:

Twin prime numbers:

As you know, the prime number is a natural number that is only divisible by 1 and itself. The prime numbers, which differ by 2 units, are called the twin prime numbers, such as (3, 5) or (11, 13).

Twin primes are pairs of primes which differ by two. The first twin primes are {3,5}, {5,7}, {11,13} and {17,19}. It has been conjectured (but never proven) that there are infinitely many twin primes.

largest twin prime pair known is:

It was discovered in September 2016. 

Mathematicians have hypothesised that there are infinitely many occurrences of twin primes; the so-called Twin Prime Conjecture. To this day, no proof has been found.

Goldbach's conjecture:

One of the most famous and oldest problems in mathematics is Goldbach's conjecture, which, despite its very simple form, has involved mathematical minds for about 270 years. The desire of every mathematician is to solve it and they do anything to solve it. Goldbach's conjecture states that :Every even integer greater than 2 can be expressed as the sum of two primes.

For example:

4 = 2 + 2

6 = 3 + 3

8 = 3 + 5

10 = 3 + 7 = 5 + 5

12 = 5 + 7

14 = 3 + 11 = 7 + 7 etc.

This conjecture was introduced in 1742 by Christine Goldbach in a letter to Leonard Euler.

this conjecture remains unresolved.

Even integers correspond to horizontal lines. For each prime, there are two oblique lines, one red and one blue. The sums of two primes are the intersections of one red and one blue line, marked by a circle. Thus the circles on a given horizontal line give all partitions of the corresponding even integer into the sum of two primes.

https://youtu.be/0SMtJaE0_-I

Perfect number:

Perfect number, a positive integer that is equal to the sum of its proper divisors. The smallest perfect number is 6, which is the sum of 1, 2, and 3. Other perfect numbers are 28, 496, and 8,128.This is followed by the perfect numbers 496 and 8128.

Rene Descartes said:"Perfect numbers like perfect men are very rare."

In January 2016, forty-ninth perfect numbers were discovered:

Are there any odd perfect numbers?

no1 knows!!!

it is not known whether there are any odd perfect numbers, nor whether infinitely many perfect numbers exist.

Collatz conjecture:

The Collatz conjecture is a conjecture in mathematics that concerns a sequence defined as follows: start with any positive integer number. Then each term is obtained from the previous term as follows: if the previous term is even, the next term is one half the previous term. If the previous term is odd, the next term is 3 times the previous term plus 1. The conjecture is that no matter what value of n, the sequence will always reach 1.

The Collatz sequence, also called the Hailstone sequence, is a sequence of numbers relevant to the Collatz conjecture, which theorizes that any number using this algorithm will eventually be reduced to 1. The conjecture's truth is supported by calculations, but it hasn't yet been proved that no number can indefinitely stay above 1.

To get a Collatz sequence from a number, if it's even, divide it by two, and if it's odd, multiply it by three and add one. Continue the operation on the result of the previous operation until the number becomes 1.

example:

number 25:

25 is odd---->(multiply it by three and add one)-->76 is even-->( divide it by two)-->38-->19-->58-->29-->88-->44-->22-->11-->34-->17-->52-->26-->13-->40-->20-->20-->5-->16-->8-->4-->2-->1

 

 

[girl_from_kurdistanX 383]

 Pi π

The pi is the ratio of the circumference of the circle to its diameter and is approximately 3.14. It does not matter what the size of the circle is; its environment 

is always 3. 14 times larger than diameter.

In the 18th century, mathematicians put the name of this constant number "Pi".

pi day

In 1988, the physicist Larry Shaw, who was in charge of the San Francisco Museum of Sciences, named March 14 as "Pi Day". But why is March 14th the day of the pi is 

also interesting, you know that March is the third month of the year, and since the number is P.3.14, March 14th is for the day.

pi is infinite number

pi is infinite number, an infinite number of digits in its decimal representation, and it does not settle into an infinitely repeating pattern of digits.

The number itself is rounded up to 3.14 but it can go on forever. On Thursday, Google confirmed it was able to compute Pi to 31.4 trillion decimal places, setting a 

new Guinness World Record. But it's more than just math.

Memorizing pi

the record for the most digits of pi memorized belongs to Rajveer Meena of Vellore, India, who recited 70,000 decimal places of pi on March 21, 2015, according to Guinness World Records. Previously, Chao Lu, of China, who recited pi from memory to 67,890 places in 2005, held the record, according to Guinness World Records.

put video The Pi Song<-------

For centuries, mathematicians were looking for a specific pattern for these figures, but in 1768 a Swiss-German mathematician, Johann Heinrich

Lambert, proved that the pi is irrational number.

How Pi was nearly changed to 3.2 :

If all of these numbers do not have any use after the end, then it is not better to consider the number of pi "3.2". In 1897, a doctor from the state of Indiana tried to establish a law to use  3.2 instead of 3.14. After much research, the parliament concluded that establishing the law to change the fixed mathematical numbers is a stupid thing!

There is an entire language made on the number Pi. But how is that possible? Well, some people love pi enough to invent a dialect in which the number of letters in the successive words are the same as the digits of pi. But it is not just another nerd quirk that nobody knows about. Mike Keith wrote an entire book, called ‘Not a Wake’ in this language.

But pi's ubiquity goes beyond math. The number crops up in the natural world, too. It appears everywhere there's a circle, of course, such as the disk of the sun, the spiral of the DNA double helix, the pupil of the eye, the concentric rings that travel outward from splashes in ponds. Pi also appears in the physics that describes waves, such as ripples of light and sound. It even enters into the equation that defines how precisely we can know the state of the universe, known as Heisenberg's uncertainty principle.

Did you know the GPS system that is on your mobile phone calculates your location with pi number?

[ZivOfficial 290]

1+1

[Cyber2_O.o 64]

Okay, I'm not sure if someone has already said something like this, but a few months ago, I just had an impulsive idea to do 61 squared (Yes, I have tons of impulsive ideas that ultimately leads to something cool/weird). And apparently, the answer to that is 3,721. 3*7=21. Cool way to remember it, huh? (Not that anyone will ever encounter that problem but still) (And yes, I have a bad habit of memorizing random math facts, mostly a two-digit number squared)

 

Oh, and while we're on the Pi Day topic, there's a site called http://mypiday.com that shows you where your birthday (or any other date) appears in Pi. It's actually pretty awesome. Mine is in the millionth or something digit of Pi.

 

And also while we're at the Pi subject, how many digits of Pi can you recite? And please be honest, don't just copy and paste it from some site (or paste it from mine). I know 3.1415926535879323846264833, but don't count on it being 100% correct.

 

Ziv, the answer to your question is... *applause, please, this question is very hard* 2 (two)! Wow, I had no idea.  ;)

[Person_Random 4,991]

3.14159265358979323846264338327950

[Guest]

Okay, I'm not sure if someone has already said something like this, but a few months ago, I just had an impulsive idea to do 61 squared (Yes, I have tons of impulsive ideas that ultimately leads to something cool/weird). And apparently, the answer to that is 3,721. 3*7=21. Cool way to remember it, huh? (Not that anyone will ever encounter that problem but still) (And yes, I have a bad habit of memorizing random math facts, mostly a two-digit number squared)

 

Oh, and while we're on the Pi Day topic, there's a site called http://mypiday.com that shows you where your birthday (or any other date) appears in Pi. It's actually pretty awesome. Mine is in the millionth or something digit of Pi.

 

And also while we're at the Pi subject, how many digits of Pi can you recite? And please be honest, don't just copy and paste it from some site (or paste it from mine). I know 3.1415926535879323846264833, but don't count on it being 100% correct.

 

Ziv, the answer to your question is... *applause, please, this question is very hard* 2 (two)! Wow, I had no idea.  ;)

That is an interesting result! Is that just a special case? I don't know Pi's digits past 3.1415.

[personia2 125]

Far out, this thread needs to learn about spoilers before they do anymore maths, just broke my fingers from scrolling so much.

[Guest]

Far out, this thread needs to learn about spoilers before they do anymore maths, just broke my fingers from scrolling so much.

Well if you are viewing this thread, then I should hope you would be fine with going through long proofs and explanations for things.

[Cyber2_O.o 64]

That is an interesting result! Is that just a special case? I don't know Pi's digits past 3.1415, however who needs infinite decimals when you can have the nice fractional representaton of Pi as 22/7?

I'm not sure. I'm currently trying to find other stuff that's cool (for example, 81 squared is 6561; 6-5=1, and add another 6 into the middle) but so far 61 was the only number that happened to have something like that.

22/7 isn't Pi's exact decimal, as it is 3.14285...