Do board games improve math skills?

We've intuitively known that most board games have a positive effect on us. Be it mental well-being, some form of learning, or even strategizing, board games contribute immensely. Given that they also help us stay away from our devices during the duration when we are playing the game, they are bound to become more popular in the future.

A new study has now validated part of what we've known intuitively, stating that board games based on numbers enhance mathematical ability among children. Their results, which is based on a comprehensive review of research published on this topic over the last 23 years, are published in the peer-reviewed journal Early Years in July.

19 studies from 2000

In order to investigate the effects of physical board games in promoting leaning, the researchers reviewed 19 studies published from 2000 onwards. These studies involved children under the age of 10 and all except one focused on the relationship between the board games and the mathematical skills of the players.

Children participating in these studies received special board game sessions led by teachers, therapists, or parents. While some of these board games were numbers-based like Snakes and Ladders and Monopoly, others did not focus on numeracy skills. These sessions were on average held twice a week for 20 minutes over two-and-a-half months.

Based on assessments on their mathematics performance before and after the intervention sessions, the studies came to their conclusions. Right from basic numeric competency like naming numbers and understanding their relationship with each other, to more complex tasks including addition and subtraction, mathematical ability received a boost in more than half the cases.

Beneficial for all learners?

 While the review established the positive effect of numbers-based board games for children, especially those young, it would be interesting to find out if such an approach would also be beneficial for all learners, including first-generation learners. By improving their fundamental understanding of numbers. children stand to gain as it helps ward off their fear of mathematics and numbers.

The study, meanwhile, also highlighted the lack of scientific evaluation to determine the impact of board games on the language and literacy areas of children. This research group plans to investigate this in their next project.

There is a need to design board games for educational purposes, both in terms of quantity and quality. The researchers believe that this is an interesting space that would open up in the coming years.

Picture Credit : Google 

HOW IS MATHS USED IN FOOTBALL?

You see the player advancing towards the goal, clearly trying to score. But the goalkeeper doesn't stand his ground. He runs towards the player instead of staying on the post. Why would he do that? The reason is maths!

Football is often referred to as "O jogo bonito", Portuguese for The beautiful game' - a nickname popularised by the Brazilian great, Pele. And rightly so.

Just like any other beautiful movement, football requires rhythm, coordination, and balance. And at the same time, it also requires skill. However, just being a master at tackling, shooting or goalkeeping does not necessarily make you a great player.

Some of the best football players on the field today are also terrific mathematicians, who use maths in football. The instinctive understanding of the concepts of geometry, speed-distance-time, and calculus which they utilise isn't determined by the ability to solve equations on a blackboard. And this application itself gives them the edge over other players. If you've watched the popular television show Ted Lasso, you will probably understand this claim by watching the coaches and players strategising how to tackle their opponents So, how is maths used in football? Let's look at calculations used by players for some of the most common goals and defence strategies in this beautiful game:

United we stand! Tiki taka football strategy

A great example of real-time use of geometry to create space and beat defenders is the tiki taka-a popular method that became the talk of town when Spain claimed the Euro Cup and the World Cup in 2008 and 2010. This is a systematic approach to football founded upon team unity and a comprehensive understanding in the geometry of space on a football field.

How do players perform tiki taka?

The football players try to form triangles all around the pitch to maintain the ball possession, making it difficult for the opponent to obtain the ball and organise their game. Tiki taka has proven to be very successful as a football strategy.

Eyes on the prize. Goalkeeper's one on one

One of the best examples where football and maths go hand in hand is distracting a striker. The goal is to create a larger obstruction to reduce the space available to score, hence lowering the probability of a goal

Often when a striker is in a one-on-one situation with the goalkeeper (like in our introduction), the latter charges towards the striker rapidly to close the space thereby reducing the angle and space available to strike the ball. This is another successful ideology of mathematical football.

How to hit a chip shot?

One of the most beautiful moves in football is chipping a charging goalkeeper. As the space reduces, the cool minded striker notices the increase in space to score. A 3-dimensional view allows the striker to kick over the charging goalkeepers head, and into the goalpost.

The chip shot, which is quite popular among both fans and players, doesn't require power, rather a deft touch that follows a perfect parabola into the net.

Know thy enemy! Save thy penalties

Teams these days are aware of the past penalties taken by players. Most players follow a pattern in their penalty shots and this analysis of the previous shots puts the keeper in a much better situation to predict the next shot.

Goal posts: to go square or to go round?

The goalposts we see now are circular and have an elliptical cross-section. The goalposts before 1987 had the square cross-section. This invariably meant that most of the shots that hit the posts, came out instead of going in which brought unnecessary disappointment to the teams.

Does football strategy need data analysts and mathematicians?

 While football maths was initially used for strategising the buying and selling of players, it is now integrated to what it can also do on the tactical analysis of the game.

Believe it or not, almost every football team today has a team of mathematicians or statisticians who help the coach define football strategies based on data. A huge amount of data is collected and analysed to understand opposing teams game-play, strengths and weaknesses of players, and to define tactics.

For example, if two players pass the ball 300 times to each other on average in a game, what kind of advantage can the opposition gain by reducing their total number of passes to 100?

Football tessellation

One very obvious example of mathematical football is the shape of the ball itself. The most familiar spherical polyhedron is the ball used in football, thought of as a spherical truncated icosahedron.

What does football tessellation mean?

 The football is usually made of white hexagon shapes and black pentagon shapes - this is an example of a tessellation figure.

WHAT IS THE RELATIONSHIP BETWEEN MATH AND SPORTS?

Behind the title-winning or record-breaking kick, hit, home run, or throw, we can uncover the mystery of maths in sports.

Sprinter Usain Bolt's world record of completing a 100-mt race in 9.58 seconds; cricketer Don Bradman's batting average of 99.94; and swimmer Michael Phelps' overall tally of 28 Olympic medals are a few statistics that indicate athletic brilliance. However, if you think about it, statistics is just one mathematical topic used in sports. For athletes, timing is everything. From finding the right corner of the goal to identifying the perfect arm angle to create history, most successful sportspeople are secret mathematicians at heart.

Let's look at five interesting aids that maths provides in sports:

1. Geometry of angle and elevation: What did David Beckham do to bend a ball? Well, timing and probably his foot staying at the perfect angle to execute that shot. If you observe his old videos, and understand the angle and the timing of the perfect free kick, then you too can bend it like Beckham!

2. The art of gaining body agility: It is important to preserve balance when you jump, spin, and dive in a pool or flip and spin effectively while performing gymnastics. The athletes must learn to be symmetrically aligned and distribute body mass. Olympics 2020's javelin throw gold medallist Neeraj Chopra's speed of projectile was calculated to be 105.52 kmph. This was a result of years of practice to acquire the posture and position to throw the javelin with the right force in the right direction and at the right angle.

3. Assess the teams and schedule tournaments: Graph theory uses geometrical diagrams to come up with the number of people or teams in a tournament along with the permutation and combination of teams that will compete with each other. For example, the FIFA World Cup based on the number of teams, the match schedule is decided such that all teams play a certain number of matches and each team gets an evenly distributed resting period.

4. Collecting data and keeping scores: You can calculate the trajectory of a running course by taking into consideration the distance of the race, lung capacity, energy intake, propulsion force, and friction. Maths is part of statistical information-from collecting data for analysis and monitoring the ongoing game to measuring the world records, which impact practice, performance, and - results in the sports world.

5. Player selection vis-a-vis budget management: Heard of Moneyball or The Art of Winning an Unfair Game? The book-turned-movie is based on the real-life story of the Oakland Athletics baseball team where the club manager and a baseball executive used equations and statistics to determine the value of players. They calculated wins needed for the postseason and runs required by using the Pythagorean theorem. In 2002, the team won the American League West Division, with a record of 103-59.

It's intriguing how maths can flip numbers and change the course of a game-from applying human intelligence or sports tech to planning tactics and predicting upcoming playoffs. Behind every title-winning or record-breaking kick, hit, home run, or throw, we can uncover the mystery of maths in sports!

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Which day is Pi (? )Day?

March 14 day is Pi Day! Pi (Greek letter "  ") is the symbol used in mathematics to represent a constant - the ratio of the circumference of a circle to its diameter - which is approximately 3.14159. Pi has been calculated to over one trillion digits past its decimal.

The first official Pi Day celebration took place on March 14, 1988, at the San Francisco Exploratorium. Noted physicist, Larry Shaw was the organiser of this event. This day got a boost when the US House of Representatives recognised March 14 as the Pi Day. The first ten digits of Pi are 3.1415926535. How many digits can a man memorise? Suresh Kumar Sharma of India set the world record and memorised 70,030 digits in 2015. 

On this day several programmes take place across the world with certain activities. Students try to solve typical mathematical problems. In educational institutions and science centres, pi memorisation challenge happens, numerical fun and quiz programmes are organised. Some of the dishes are named on pi such as pizza pie, fruit pie and so on. This celebration aims to enhance the interest of people in mathematics and physics.

Credit : Maps of India

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What is the importance of mathematics in our daily lives?

You think maths is useful only as part of one's academic life? Actually, maths helps us do many important tasks in our daily life.

1. Time and task management skills: When we wake up in the morning, we look at the time to see whether we have enough time to complete various tasks. Additionally, we use maths when it comes to reading a clock / watch or planning one's tasks. Maths is the primary factor in managing time while completing various tasks in our daily lives.

2. Budgeting and dealing with money: Managing money, understanding discounts, and buying for the best price all involve the knowledge of maths and, at least, a basic understanding of how percentages work. Here's an example. How much would a shirt or blouse cost once a 50 % discount is applied? What about once the taxes are added? These questions can be answered only once we understand how discounts and percentages work.

3. Understanding your favorite sports activity: Basic knowledge of maths also helps keep track of scores for every sports activity. Geometry and trigonometry can also help students find the best way to hit a ball, make a basket, or run around the track in an effective manner.

4. Baking your favorite pie: Measuring the ingredients to add to a recipe and kitchen inventory planning require an understanding of fractions and conversion. For example, if the recipe calls for two cups, but you only have a quarter-cup measuring tool and a half-cup measuring tool, how much adds up to two?

5. Home decor and interior designing: A fair knowledge of dimensions, units, and unit conversions is required to be able to sail through any basic home decoration. Common questions when you are trying to set up your new space or apartment could range from the dimensions of wallpaper needed for a wall to having enough space to fit your favorite couch. It's very important to know these basics before you head to a store.

6. Exercising and dieting: We set our routine according to our workout schedule, count the number of repetitions while exercising, etc., just based on maths. Additionally, we set up diet and meal plans based on effective management of time and meals.

7. Driving: Operating a car or motorcycle is ultimately nothing but a series of calculations with respect to the number of km to the destination, the amount of petrol in the vehicle, the distance that can be covered in a given amount of time or per litre of fuel, how a traffic jam can slow the pace, etc.

8. DIY clothing and design: Maths is also an essential aspect of designing. From taking measurements and estimating the quantity of clothes to producing clothes according to one's needs and tastes, maths is followed at every stage.

9. Critical thinking: Technically, 'critical thinking' is not even maths as there are no numbers involved. However, knowledge of maths surely increases the ability to think critically. The more maths skills you gain, the more you observe the minute details, question available data, rule out unnecessary data, and analyse it for your benefit.

10. The base of other subjects: Although maths is a unique subject, it also forms the base for every other subject, including physics, chemistry, economics, history, accountancy, and statistics.

Maths is a tool in our hands to make our lives easier and more seamless. The more mathematical we are in our approach, the more rational would be our thoughts.

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What is the main concept of Rhind papyrus in the Egyptian mathematical system?

The Rhind Mathematical Papyrus is the best example of Egyptian mathematics. Dating back to 1650 BC, it was copied by an Egyptian scribe named Ahmes from another document written around 2000 BC. It is named after Alexander Rhind, a Scottish antiquarian, who purchased the papyrus in 1858 in Luxor, Egypt. The papyrus is 33 cm tall and 5 m long and contains 87 mathematical problems as well as the earliest reference to Pi.

The Pharaoh’s surveyors used measurements based on body parts (a palm was the width of the hand, a cubit the measurement from elbow to fingertips) to measure land and buildings very early in Egyptian history, and a decimal numeric system was developed based on our ten fingers. The oldest mathematical text from ancient Egypt discovered so far, though, is the Moscow Papyrus, which dates from the Egyptian Middle Kingdom around 2000 – 1800 BCE.

It is thought that the Egyptians introduced the earliest fully-developed base 10 numeration system at least as early as 2700 BCE (and probably much early). Written numbers used a stroke for units, a heel-bone symbol for tens, a coil of rope for hundreds and a lotus plant for thousands, as well as other hieroglyphic symbols for higher powers of ten up to a million. However, there was no concept of place value, so larger numbers were rather unwieldy (although a million required just one character, a million minus one required fifty-four characters).

The Rhind Papyrus, dating from around 1650 BCE, is a kind of instruction manual in arithmetic and geometry, and it gives us explicit demonstrations of how multiplication and division was carried out at that time. It also contains evidence of other mathematical knowledge, including unit fractions, composite and prime numbers, arithmetic, geometric and harmonic means, and how to solve first order linear equations as well as arithmetic and geometric series. The Berlin Papyrus, which dates from around 1300 BCE, shows that ancient Egyptians could solve second-order algebraic (quadratic) equations.

Practical problems of trade and the market led to the development of a notation for fractions. The papyri which have come down to us demonstrate the use of unit fractions based on the symbol of the Eye of Horus, where each part of the eye represented a different fraction, each half of the previous one (i.e. half, quarter, eighth, sixteenth, thirty-second, sixty-fourth), so that the total was one-sixty-fourth short of a whole, the first known example of a geometric series. Unit fractions could also be used for simple division sums.

The Egyptians approximated the area of a circle by using shapes whose area they did know. They observed that the area of a circle of diameter 9 units, for example, was very close to the area of a square with sides of 8 units, so that the area of circles of other diameters could be obtained by multiplying the diameter by 8?9 and then squaring it. This gives an effective approximation of ? accurate to within less than one percent.

The pyramids themselves are another indication of the sophistication of Egyptian mathematics. Setting aside claims that the pyramids are first known structures to observe the golden ratio of 1 : 1.618 (which may have occurred for purely aesthetic, and not mathematical, reasons), there is certainly evidence that they knew the formula for the volume of a pyramid – 1?3 times the height times the length times the width – as well as of a truncated or clipped pyramid.

They were also aware, long before Pythagoras, of the rule that a triangle with sides 3, 4 and 5 units yields a perfect right angle, and Egyptian builders used ropes knotted at intervals of 3, 4 and 5 units in order to ensure exact right angles for their stonework (in fact, the 3-4-5 right triangle is often called “Egyptian”).

Credit : Story of Mathematics 

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How is mathematics used in kitchen?

Have you ever wondered how the food that lands up on your plate is made? No, we are not talking about the journey of rice or other materials from the time they are sowed in fields till the time they are cooked into food. Instead, we are talking about how food is prepared in the kitchen, either by those cooking at home, or the chefs who prepare the food in hotels.

Culinary math is here

Culinary math is an emerging field that combines kitchen science with mathematics. At the heart of this subject is the understanding that appealing meals aren’t made by just combining ingredients in a haphazard manner. A great cook, in fact, has a lot in common with a scientist and a mathematician.

This is because what is made to look carefree and spontaneous in cookery shows is actually the result of years of hard work and practice. Cooking routines include simple to complex mathematical calculations. From counting portions to increasing the yield when required, there are numbers at play during various stages of the meal.

Computation and geometry

While addition, subtraction, multiplication, division, and fractions are involved while computing and working with the ingredients, ratios, percentages, and yields come into the picture when deciding the total amount of a food to be cooked, and then distributing them to people.

When working with spherical roti doughs and cubic paneer portions, a cook is knowingly or unknowingly dabbling with geometry. And by being familiar with units and abbreviations of measurements, and fluently converting them from one system to another, the person who is cooking is also able to borrow from cuisines from abroad.

A number of courses in culinary math has started to develop around the world, targeting students who aim to become chefs in high-end hotels. For, even though it might seem as if a famous chef is just sprinkling a bit of this, grabbing a pinch of that, and garnishing with a little bit of something else, there is a lot of maths applied to it, knowing which makes it easier.

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Why always add, when we can also subtract?

What do you do when you find yourself in a sticky situation and you need to find a solution? Do you try to add some element to it in the hope that it would improve the overall situation? If so, you are not alone. A recent study shows that when people are looking to improve a situation, idea or object, an overwhelming majority of them try to add something to it, irrespective of whether it helps or not. This also means that people never stop to think and remove something as a solution, even if it might actually work.

In order to understand this better, think about all the adults working from home during the ongoing pandemic. You must have noticed that many of them, maybe even your parents, have complained about attending endless meetings that eat into their schedule, giving them little time to do actual work. This is a classic case of adding more and more meetings to make up for office environment, with little thought going into whether all those meetings are actually required. A simpler solution might have been to stick to existing schedules or maybe even cutting down some meetings (consider the fatigue involved in video calls as opposed to face-to-face encounters) and making communication within an organisation more efficient.

In a paper that featured in Nature, researchers from the University of Virginia looked at why people overlook subtractive ideas altogether in all kinds of context. They stated that additive ideas come more quickly and easily, whereas subtractive ones need more effort. As we are living in a fast-paced world where we are likely to implement the first ideas that occur to us, this means that additive solutions are largely accepted, without even considering subtractive ones.

Self-reinforcing effect

This further has a self-reinforcing effect. As we rely more and more on additive ideas, they become more easily accessible to us. With time, this becomes a habit, meaning our brains have a strong urge to look for additive ideas. As a result, the ability to improve the world through subtractive strategies is lost on us.

While the interesting finding of the research, which has overlaps between behavioural science and engineering, could have plenty of application across sectors, researchers believe it could be particularly useful in how we harness technology.

Less is more

The results highlight humanity’s overwhelming focus on always adding, even when the correct answer might actually to be subtract something. While this holds true for everything from people struggling with overfull schedules to institutions finding it hard to adhere to more and more rules, it also shows how we are inherently geared towards exhausting more of our planet’s resources. A minimalist approach of less is more might word wonders in a lot of situations.

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What is knot theory?

Have you ever wondered if there is more to knots than meets your eye when tying your shoelaces? If so, here’s your answer: there’s a theory in mathematics called knot theory that delves into exactly this.

Study of closed curves

Knot theory is the study of closed curves in three dimensions and their possible deformations without one part cutting through another. Imagine a string that is interlaced and looped in any manner. If this string is then joined at the ends, then it is a knot.

The least number of crossings that occur even as a knot is moved in all possible ways denotes a knot’s complexity. This minimum number of crossings is called the order of the knot and the simplest possible knot has an order of three.

More crossings, more knots

As the order increases, the number of distinguishable knots increases manifold. While the number of knots with an order 13 is around 10,000, that number jumps to a million for an order of 16.

German mathematician Carl Friedrich Gauss took the first steps towards a mathematical theory of knots around 1800. The first attempt to systematically classify knots came in the second half of the 19th Century from Scottish mathematician-physicist Peter Guthrie Tait.

While the knot theory continued to develop for the next 100 years or so as a pure mathematical tool, it then started finding utility elsewhere as well. A breakthrough by New Zealand mathematician Vaughan Jones in 1984 allowed American mathematical physicist Edward Witten to discover a connection between knot theory and hyperbolic geometry. Jones, Witten, and Thurston all won the Fields medal, considered to be among the highest prizes for mathematics, for their contributions.

Many applications

These developments in the last few decades has meant that knot theory has found applications in biology, chemistry, mathematical physics, and even cosmology. Who knows, the possibilities with knots could possibly be endless.

 

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In mathematics, how do you know when you have proven a theorem?



Two things: You learn that you don’t know, and you learn that deep inside, you do.



When you find, or compose, or are moonstruck by a good proof, there’s a sense of inevitability, of innate truth. You understand that the thing is true, and you understand why, and you see that it can’t be any other way. It’s like falling in love. How do you know that you’ve fallen in love? You just do.



Such proofs may be incomplete, or even downright wrong. It doesn’t matter. They have a true core, and you know it, you see it, and from there it’s only a matter of filling the gaps, cleaning things up, eliminating redundancy, finding shortcuts, rearranging arguments, organizing lemmas, generalizing, generalizing more, realizing that you’ve overgeneralized and backtracking, writing it all neatly in a paper, showing it around, and having someone show you that your brilliant proof is simply wrong.



And this is where you either realize that you’ve completely fooled yourself because you so wanted to be in love, which happens more often when you’re young and inexperienced, or you realize that it’s merely technically wrong and the core is still there, pulsing with beauty. You fix it, and everything is good with the world again.



Experience, discipline, intuition, trust and the passage of time are the things that make the latter more likely than the former. When do you know for sure? You never know for sure. I have papers I wrote in 1995 that I’m still afraid to look at because I don’t know what I’ll find there, and there’s a girl I thought I loved in 7th grade and I don’t know if that was really love or just teenage folly. You never know.



Fortunately, with mathematical proofs, you can have people peer into your soul and tell you if it’s real or not, something that’s harder to arrange with crushes. That’s the only way, of course. The best mathematicians need that process in order to know for sure. Someone mentioned Andrew Wiles; his was one of the most famous instances of public failure, but it’s far from unique. I don’t think any mathematician never had a colleague demolish their wonderful creation.



Breaking proofs into steps (called lemmas) can help immensely, because the truth of the lemmas can be verified independently. If you’re disciplined, you work hard to disprove your lemmas, to find counterexamples, to encourage others to find counterexamples, to critique your own lemmas as though they belonged to someone else. This is the very old and very useful idea of modularization: split up your Scala code, or your engineering project, or your proof, or what have you, into meaningful pieces and wrestle with each one independently. This way, even if your proof is broken, it’s perhaps just one lemma that’s broken, and if the lemma is actually true and it’s just your proof that’s wrong, you can still salvage everything by re-proving the lemma.



Or not. Maybe the lemma is harder than your theorem. Maybe it’s unprovable. Maybe it’s wrong and you’re not seeing it. Harsh mistress she is, math, and this is a long battle. It may takes weeks, or months, or years, and in the end it may not feel at all like having created a masterpiece; it may feel more like a house of sand and fog, with rooms and walls that you only vaguely believe are standing firm. So you send it for publication and await the responses.



Peer reviewers sometimes write: this step is wrong, but I don’t think it’s a big deal, you can fix it. They themselves may not even know how to fix it, but they have the experience and the intuition to know that it’s fine, and fixing it is just work. They ask you politely to do the work, and they may even accept the paper for publication pending the clean up of such details.



There are, sometimes, errors in published papers. It happens. We’re all human. Proofs that are central have been redone so many times that they are more infallible than anything of value, and we can be as certain of them as we are certain of anything. Proofs that are marginal and minor are more likely to be occasionally wrong.



So when do you know for sure? When reviewers reviewed, and time passes, and people redo your work and build on it and expand it, and over time it becomes absolutely clear that the underlying truth is unassailable. Then you know. It doesn’t happen overnight, but eventually you know.



And if you’re good, it just reaffirms what you knew, deep inside, from the very beginning.



Mathematical proofs can be formalized, using various logical frameworks (syntactic languages, axiom systems, inference rules). In that they are different from various other human endeavors.



It's important to realize, however, that actual working mathematicians almost never write down formal versions of their proofs. Open any paper in any math journal and you'll invariably find prose, a story told in some human language (usually English, sometimes French or German). There are certainly lots of math symbols and nomenclature, but the arguments are still communicated in English.



In recent decades, tremendous progress has been made on practical formalizations of real proofs. With systems like Coq, HOL, Flyspeck and others, it has become possible to write down a completely formal list of steps for proving a theorem, and have a computer verify those steps and issue a formal certificate that the proof is, indeed, correct.



The motivation for setting up those systems is, at least in part, precisely the desire to remove the human, personal aspects I described and make it unambiguously clear if a proof is correct or not.



One of the key proponents of those systems is Thomas Hales, who developed an immensely complex proof of the Kepler Conjecture and was driven by a strong desire to know whether it's correct or not. I'm fairly certain he wanted, first and foremost, to know the answer to that question himself. Hales couldn't tell, by himself, if his own proof is correct.



It is possible that in the coming decades the process will become entirely mechanized, although it won't happen overnight. As of 2016, the vast majority of proofs are still developed, communicated and verified in a very social, human way, as they were for hundreds of years, with all the hope, faith, imprecision, failure and joy that human endeavors entail.



 



Credit : Quora



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What is the story of taxicab numbers?



Are you aware of numbers that are called as taxicab numbers? The nth taxicab number is the smallest number representable in n different ways as a sum of two positive integer cubes. These numbers are also called as the Hardy-Ramanujan number. The name taxicab numbers, in fact is derived from a story told about Indian mathematician Srinivasa Ramanujan by English mathematician GH Hardy. Here is the story, as told by Hardy I remember once going to see him (Ramanujan) when he was lying ill at Putney. I had ridden in taxi-cab No. 1729, and remarked that the number seemed to be rather a dull one, and that I hoped it was not an unfavourable omen. "No," he replied, "it is a very interesting number, it is the smallest number expressible as the sum of two [positive] cubes in two different ways."



1729, naturally, is the most popular taxicab number. 1729 can be expressed as the sum of both 12^3 and 1^3 (1728+1) and as the sum of 10 and 9 (1000+729).



While the story involving Ramanujan made these numbers famous and also gave it its name. these numbers were actually known earlier. The first mention of this concept can be traced back to the 17th Century.



2 (1^3 + 1^3) is the first taxicab number and 1729 is the second. The numbers after 1729 have been found out using computers and six taxicab numbers are known so far.



 



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What is the product of all the numbers that appear in the dial pad of our mobile phones?



Since one of the numbers on the dial of a telephone is zero, so the product of all the numbers on it is 0.



The layout of the digit keys is different from that commonly appearing on calculators and numeric keypads. This layout was chosen after extensive human factors testing at Bell Labs. At the time (late 1950s), mechanical calculators were not widespread, and few people had experience with them. Indeed, calculators were only just starting to settle on a common layout; a 1955 paper states "Of the several calculating devices we have been able to look at... Two other calculators have keysets resembling [the layout that would become the most common layout].... Most other calculators have their keys reading upward in vertical rows of ten," while a 1960 paper, just five years later, refers to today's common calculator layout as "the arrangement frequently found in ten-key adding machines". In any case, Bell Labs testing found that the telephone layout with 1, 2, and 3 in the top row, was slightly faster than the calculator layout with them in the bottom row.



The key labeled ? was officially named the "star" key. The original design used a symbol with six points, but an asterisk (*) with five points commonly appears in printing.[citation needed] The key labeled # is officially called the "number sign" key, but other names such as "pound", "hash", "hex", "octothorpe", "gate", "lattice", and "square", are common, depending on national or personal preference. The Greek symbols alpha and omega had been planned originally.



These can be used for special functions. For example, in the UK, users can order a 7:30 am alarm call from a BT telephone exchange by dialing: *55*0730#.



 



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What is a zero in math?



Do you have a mathematics teacher who writes a big fat zero that occupies the entire blackboard whenever an answer boils down to it? None of us wish to see it on our answer sheets (unless, of course, it is for 100). but zero fascinates and frustrates maths lovers and haters in equal measures. Even though civilisations have always understood the concept of nothing or having nothing. India is generally credited with developing the numerical zero. It is hard for us to imagine a world without zero, and it is no wonder therefore that giving zero a symbol is seen as one of the greatest innovations in human history. Without this zero, modem mathematics, physics and technology would all probably zero down to nothing! The philosophy of emptiness or shunya (shunya is zero in Sanskrit) is believed to have been an important cultural factor for the development of zero in India. The concept is said to have been fully developed by the 5th Century. and maybe even earlier.



The Bakhshali manuscript, discovered in a field in 1881, is currently seen as the earliest recorded use of a symbol for zero. Dating techniques place this manuscript to be written anywhere between the 3rd and 9th Century.



 



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What do you call a triangle with one angle over 90 degrees but under 180 degrees?



An obtuse-angled triangle is a triangle in which one of the interior angles measures more than 90° degrees. In an obtuse triangle, if one angle measures more than 90°, then the sum of the remaining two angles is less than 90°. 



Special facts about obtuse triangle:




  • An equilateral triangle can never be obtuse. Since an equilateral triangle has equal sides and angles, each angle measures 60°, which is acute. Therefore, an equilateral angle can never be obtuse-angled.

  • A triangle cannot be right-angled and obtuse angled at the same time. Since a right-angled triangle has one right angle, the other two angles are acute. Therefore, an obtuse-angled triangle can never have a right angle; and vice versa. 

  • The side opposite the obtuse angle in the triangle is the longest. 



In our surroundings, we can find many examples of obtuse triangles. Here are some examples:




  • Triangle shaped roofs 

  • Hangars found in cupboards



 



Picture Credit : Google


WHO WAS PYTHAGORAS?


Pythagoras was a Greek living in the sixth century BC. He was a mathematician and scientist who are now best remembered for Pythagoras’ Theorem, a formula for calculating the length of one side of a right-angled triangle if the other sides are known. However, this theorem was, in fact, already known hundreds of years earlier by Egyptian and Babylonian mathematicians.



Pythagoras was a Greek philosopher who was born in Samos in the sixth century B.C. he was a great mathematician who explained everything with the help of numbers. He gave the Pythagorean Theorem. The Pythagorean Theorem states that the sum of the squares of the lengths of legs of any right angled triangle is equal to the square of the length of its hypotenuse. The hypotenuse is known to be the longest side and is always equal opposite to the right angle.



The theorem can be written as an equation where lengths of the sides can be a, b and c. The Pythagorean equation is a2 + b2 = c2 where c is the length of the hypotenuse and a, b are lengths of the two sides of the triangle. The Pythagorean equation simplifies the relation of the sides of the right triangle to each other in such a way that if the length of any of the two sides of the right triangle is known, then the third side can be easily found.



To generalise this theorem, there is the law of cosines which helps in calculation of the length of any of the sides of the triangle when the other two lengths for the two sides are given along with the angle between them. When the angle between the other sides turns out to be a right angle, then the law of the cosines becomes the Pythagorean Theorem. The converse of this theorem is also true. It is that for any triangle with sides a, b and c, if a2 + b2 = c2, then the angle between the two sides a and b would turn out to be 900.



Picture Credit : Google