Merry ChristMATHS๐ŸŽ„๐Ÿ˜

Before you find your seat at the dinner table today, why not do a bit of maths to ensure youโ€™re a winner…the maths for winning the cracker pull every time ๐Ÿ˜

There is a mathematical formula you can follow to win a Christmas cracker pull ๐ŸŽ‰. It has been found that the best way to pull a cracker is to pull down and at an angle โ†˜๏ธ given by the following formula:

angle = (11 x cracker circumference)/cracker length + 5 x cracker quality,
where the cracker quality is a number between 1-3 (1 for low quality and 3 for high quality). This angle should be somewhere between 20-55 degrees.
Another fun ChristMATHS fact๐ŸŽ„๐Ÿ‘€ if you were to add up all of the gifts that your true love gave to you in the 12 days of Christmas ๐ŸŽต you would get one for each day of the year except for Christmas Day ๐Ÿคฏ๐ŸŽ #christmas#maths#appliedmathematics#christmascrackers#12daysofchristmas#mathsinlife#winningstrategies#usingmaths#scicomm#merrychristmas

Using maths to combat bacterial infections ๐Ÿฆ 

Let’s suppose you eat some undercooked meat ๐Ÿ— or drink some contaminated water๐Ÿฅ› by mistake. You might be fine, you might feel a bit sick for a few days but get better, but (if you are unlucky) you might have to go to the hospital and have a course of antibiotics ๐Ÿ’Š.

Let’s talk about what happens inside your body when you get a bacterial infection. Your body recognises the bacteria as an ‘enemyโ€™ and so produces chemicals that attract cells called white blood cells. Once white blood cells reach the bacteria, they engulf (eat) the bacteria until the infection is defeated (cleared). If the white blood cells can’t do this on their own, then antibiotics can help by either killing the bacteria or preventing them from replicating. Many types of bacteria, however, have some tricks up their sleeves to prevent such an easy defeat๐Ÿ‘Š๐Ÿผ. For example, certain types of E. coli are able to hide from the immune system. The details of how the immune system interacts with bacteria is not always well understood…this is where maths comes to the rescue!๐ŸŽ‰

We can model an infection by writing mathematical equations and algorithms (rules) that describe what happens in the infection, based on what we already know about the biology ๐Ÿงฌ. For example, we could say that white blood cells move around randomly until some of those chemicals show up, and then the white blood cells would move in the general direction of the bacteria. Once we have made our model, we then ‘press playโ–ถ๏ธ’ to watch a simulation of the infection. Incorporating the impact of different antibiotic strategies on the rate of infection clearance in these simulations, can help us to decide which strategies are best.

These models can even be used to test the ability of made up drugs and strategies to clear infections (which is clearly much safer than testing these on people!). Using maths also saves on much of the money ๐Ÿ’ต and time โฐ that would be spent in doing physical experiments ๐Ÿงซ.

Research on this topic was undertaken by James Preston during his PhD at the University of Nottingham๐Ÿ™Œ๐Ÿป

#appliedmathematicsย #bacteriaย #mathmodelingย #mathsinlifeย #antibioticsย #scicomm

What would happen if our planet started spinning the other way?! ๐ŸŒ๐Ÿ‘€ Maths can tell us ๐Ÿ˜ƒ

Like most planets in our solar system, if we were sat above the North Pole looking down on the Earth, we would see it rotating in an anti clockwise direction ๐Ÿ”„. The forces involved in this spinning motion have shaped the environments and climates that we live in. But what would happen if it rotated the other way?๐Ÿค”๐Ÿค”

Well mathematical equations can be used to model the changes in Earths atmosphere and oceans over time (this is how we can have weather forecasts! ๐ŸŒฆ). One of these models is called the Earth System Model (ESM) and this has been used to predict what our planet might be like (the temperature๐Ÿ”ฅ, wind speeds๐ŸŒช, currents๐ŸŒŠ, moisture๐Ÿ’ง, concentrations of gases๐ŸŒซ, land use๐Ÿ„ etc…) in many years to come. There are a lot of measurements to consider over a whole lot of space (the entire Earth!๐ŸŒ), so to make this a little easier the Earth is divided into a 3D grid๐ŸŒ (across its surface and in the vertical direction). Even so, however, these equations can only be solved using supercomputers! ๐Ÿฆธโ€โ™‚๏ธ๐Ÿ’ป

So if we reverse the direction of the spin in these simulations, we can also use this model to test what would happen in this strange scenario ๐Ÿ‘€. As expected, it is found that countries would experience new climatic conditions due to changes in winds and currents. But it also turns out that if the Earth was rotating clockwise ๐Ÿ”, we would have fewer deserts and more forests. This would mean more plant life ๐ŸŒฑ and more stores of carbon (which could reduce warming from climate change!)

#appliedmathematicsย #theplanetsย #earthย #rotationย #backwardsย #mathsinspaceย #usingmathsย #climatechangeย #weatherย #simulationย #mathmodelingย #predictionsย #scicomm

Weird &Wonderful random maths fact ๐Ÿ‘€ Pokemon is packed full of maths!

Pokemon is a popular battle game played by so many – but do you realise how much maths it uses?? ๐Ÿค”

When one Pokemon defeats another in battle, they gain experience points. Once enough experience points have been gained, the Pokemonโ€™s level increases, which in turn makes the Pokemon stronger, faster and harder to knock out ๐Ÿ‘Š๐Ÿผ. Equations are used to decide how many experience points a Pokemon needs to advance to the next level. There are different equations for different Pokemon, making some easier to raise than others. Furthermore, there is a formula that decides how many experience points a Pokemon gains when it wins a fight. This equation depends on the level of the opponent, as well as the species of the opponent Pokemon.

There are many other complicated equations involved in this game, including the equation that decides how much damage an attack does (based on the attack strength, opponent defence strength, move power, types of Pokemon and even a bit of luck ๐Ÿ€)

Probability also appears in many aspects of the game, including the chance of an attack successfully hitting ๐ŸŽฏ, the chance of encountering a specific Pokemon in the wild (stronger or more rare pokemon have a smaller chance of being encountered) and the chance of a wild Pokemon successfully being caught.

So if you fancy a job designing video games for a company such as Nintendo, a strong understanding of algebra and probability is very important! ๐Ÿ‘ฉ๐Ÿผโ€๐Ÿ’ป๐Ÿ‘จ๐Ÿฝโ€๐Ÿ’ป

#appliedmathematicsย #computergamingย #gameboyย #switchย #pokemonย #pokemonswordshieldย #pokemonrbyย #pikachuย #bulbapediaย #pokeballย #usingmathsย #scicomm

Using maths to lower the cost of space travel ๐Ÿš€ ๐Ÿ‘€

With current advances in technology, exploring our solar system is easier than it has ever been. But these missions are still quite rare since the amount of money needed for space travel remains very high! ๐Ÿ’ต๐Ÿ’ต A mathematical concept called the Arnold diffusion mechanism (Iโ€™ll explain this later), however, is being used to reduce the amount of fuel needed for these trips (one of the major costs of space travel ๐Ÿ’ต) by finding the most efficient routes (those that need the least fuel).

But the most efficient route is in a straight line right?! ๐Ÿค” Well this is usually the case on earth but, with the gravitational forces present in space, a straight path isnโ€™t always the best idea. Each planet and their moons ๐ŸŒ“ as well as stars โญ๏ธ and asteroids โ˜„๏ธ have gravitational forces surrounding them which pull the rockets without the need to use fuel. By using this, strange looping routes actually become more efficient than straight routes through space. So back to the Arnold diffusion concept – the idea is that if a small amount of force from the engine is applied at the right time and location, then it has a big impact on the movement of the rocket. Maths can be used, therefore, to find the precise times and positions, where a small fire of the engine will be enough to give large distances of space travel.๐Ÿš€

#space#usingmaths#appliedmathematics#science#stem#savingmoney#reducingfuels#rocket#solarsystem#keeplearning#mathsconcepts#scicomm

Using the maths of fire ant colonies to help with engineering, construction and robotics ๐Ÿœ๐Ÿœ๐Ÿœ๐Ÿœ๐Ÿœ๐Ÿ‘Œ๐Ÿป

Colonies of fire ants are big on team work! During floods for example they have been found to form rafts by connecting together in a thick mass so that the water doesnโ€™t get through! In a similar way, they can also build themselves into towers, balls or bridges when they need to help their fellow team mates.๐Ÿ’ช๐Ÿฝ

Within these masses each ant grabs onto their neighbours using sticky padded feet but they also constantly change neighbours so that they are always moving. When forming structures like a bridge therefore, any cracks are quickly healed by new ants filling these spaces. ๐Ÿœ ๐Ÿœ ๐Ÿœ –

We can use maths to figure out the rules of fire ant colony behaviours so that we can copy these in some pretty useful ways! This is done by modelling the changes in the positions of ants in a colony, including how they respond to stresses as well as their speed and movements when swapping neighbours.

Knowing these things could massively help us in different areas of engineering including in developing robots that self assemble ๐Ÿค– and bridges that automatically fix cracks ๐ŸŒ‰.

#appliedmathematics#mathsinlife#usingmathinreallife#mathsinnature#ants#bridges#buildingbridges#selfhealing#robot#engineering#keeplearning#stem#scicomm

Weird & Wonderful random maths fact ๐Ÿ‘€ ๐Ÿ’ณ

There are 4 simple steps that anyone can take to check if a credit card number is real! ๐Ÿ’ณ

Credit cards have 16 numbers. The first 15 are decided by the bank but the last number uses a mathematical algorithm based on the other numbers. This โ€œcheck digitโ€ is used to check a credit card number is correct and that no errors have been made. โœ…

Follow the steps below with your credit card number to check this works! ๐Ÿค—

1. Beginning with the check digit (last digit), double every 2nd number (i.e. double the number to the left of the check digit and every other number after that, working from right to left)

2. If any of the answers to the above gives a 2 digit number then add these 2 numbers together (i.e. 14 โžก๏ธ 1+4=5)

3. Add up all these values plus the digits of the credit card number that were not doubled to get one number.

4. Adding the value of the check digit to this number should give a value that is divisible by 10! So if you didnโ€™t already know your check number then you can find it by working out the 1 digit number you would need to add to your answer to give a multiple of 10! ๐Ÿ‘€๐Ÿ™Œ๐Ÿป (i.e. if your answer is 46 then your check digit should be 4!)

#mathsinlife#usingmaths#appliedmathematics#algorithm#creditcard#numbers#check#tryathome#stem#keeplearning#scicomm

The Maths of Crowds ๐Ÿ‘ฉโ€๐Ÿ‘ฉโ€๐Ÿ‘งโ€๐Ÿ‘ฆ๐Ÿ‘จโ€๐Ÿ‘ฉโ€๐Ÿ‘งโ€๐Ÿ‘ง๐Ÿ‘จโ€๐Ÿ‘จโ€๐Ÿ‘งโ€๐Ÿ‘ง๐Ÿ‘จโ€๐Ÿ‘จโ€๐Ÿ‘ฆโ€๐Ÿ‘ฆ๐Ÿ‘ฉโ€๐Ÿ‘ฆโ€๐Ÿ‘ฆ๐Ÿ‘จโ€๐Ÿ‘ฉโ€๐Ÿ‘ง

You may think that, given a large number of people in a crowd, it is impossible to know how these people will move. Everyone has free will right?! and so we couldn’t possibly know what will happen. Well people are more predictable than you may know. By coming up with some basic behaviours that people are assumed to follow, mathematical equations have been made to predict the motion of people in crowds.๐Ÿ™Œ๐Ÿป So lets imagine a situation – how about you are simply shopping in a busy town centre like the one in the image. We are assumed to follow these general behaviours:

1: People have a target place that they want to get to (your favourite shop might have a sale on!๐Ÿ‘€๐Ÿƒ๐Ÿผโ€โ™‚๏ธ๐Ÿ‘›๐Ÿ›)

2: There is some randomness in the way people move (would be pretty hard to walk in a completely straight line with lots of people around)

3: People can’t walk through obstacles like walls (unfortunately ๐Ÿ˜ค)

4: People that are with people they know will want to walk close to them (most people like to talk to the people that they go shopping with ๐Ÿ‘ซ)

5: People won’t want to get too close to strangers (can be a little awkward and uncomfortable ๐Ÿ˜ณ)

Using these behaviours, in what is called an Agent Based Model, can be important in ensuring safety in crowd situations. Overcrowding is exteremely dangerous and can lead to serious injury. These models are used in many situations where you might expect lots of people (such as at a football match or in the London underground) in order to ensure the design of the space is safe for that number of people.

Similar models have also been made to explain the movement of a flock of birds ๐Ÿฆ… ๐Ÿฆ… ๐Ÿฆ… or a shoal of fish ๐ŸŸ ๐ŸŸ ๐ŸŸ . Though I don’t think birds (or fish for that matter) are keen shoppers, rules they may follow are not too different. For example they want to fly close to each other to stay in the flock but not too close so they can avoid a crash.

#matharoundus#usingmaths#appliedmathematics#collectivebehavior#crowds#shoaloffish#flockofbirds#modelling#agentbasedmodeling#crowdsafety#stem#scicomm#keeplearning

The maths of hallucinations ๐Ÿง ๐Ÿ‘€

Have you ever seen something briefly that you then realise wasnโ€™t actually there? Or rubbed your eyes and seen patterns dancing on your eyelids?๐Ÿ‘These are called visual hallucinations and they happen when your brain is trying to make sense of the information it receives from your eyes.ย  Your brain uses this information but also fills in the gaps based on what you have seen before.ย  What we think we see, therefore, may actually be slightly different to what is actually there.๐Ÿค” Mathematical equations can be used to look at the changes in activity of neurons (brain cells) across the part of the brain that first gets the information from the eyes.ย  By comparing these patterns of activity with the patterns of the hallucinations that are seen, we can better understand how hallucinations happen and predict other hallucinations that may occur. Maths can also help us to learn more about hallucination causing illnesses such as schizophrenia, Parkinsonโ€™s or epilepsy.๐Ÿ‘๐Ÿป Using maths takes us one step closer to understanding the most complex structure in the universe.๐Ÿง ๐Ÿค— What do you see when looking at the image above?๐Ÿ‘€๐Ÿ‘€ This research is being undertaken by Abigail Cocks at the University of Nottingham.๐Ÿ™Œ๐Ÿปย #appliedmathematicsย #neuroscienceย #brainย #hallucinationsย #mathsinlifeย #mathsinnatureย #mathsinmedicineย #stemย #womeninmathematicsย #scicommย #keeplearning

Using maths to find the culprit!๐Ÿง The statistics of text ๐Ÿ“– ๐Ÿ“š ๐Ÿ“„๐Ÿ—ž

Did you know that maths can be used to find patterns in text in order to help police find out who wrote a ransom note?? ๐Ÿง๐Ÿ‘ฎ๐Ÿผโ€โ™€๏ธ Text can be represented as mathematical structures called networks. Networks are made up of things called nodes and edges, we can think of nodes as houses ๐Ÿ  that may or may not be connected by paths ๐Ÿ˜ or edges. For a piece of text, each word is a node of the network and these are joined to each other by edges when words appear near each other in the text. By comparing patterns in networks like these, it is possible to determine the gender, education level and even personality traits of the writer of the ransom note! This information can then narrow down the search for the culprit! ๐Ÿ•ต๐Ÿปโ€โ™‚๏ธ – –
Using statistics on text actually makes a lot of sense since this would take far too long for us to do ourselves. For example, to decide if an email is spam, the computer must have looked at thousands of emails and found a pattern in what makes a โ€˜spam emailโ€™. A person wouldnโ€™t have time to sit and go through every email to decide what is spam, so we need to train a machine to do this for us automatically using statistics ๐Ÿ’ป

Other examples of uses of this technique include in plagiarism detection and in comparing novels written by different authors. This work is being undertaken by Katie Severn at the University of Nottingham ๐Ÿ™Œ๐Ÿป – –
#appliedmathematics#mathsandliterature#mathsinlife#statistics#whodoneit#findingtheculprit#networks#womeninmaths#girlsinstem#scicomms#communicatingscience#maths#keeplearning