Breakfast maths ๐Ÿฅฃ๐Ÿ˜‹

Why are the large nuts always at the top of the cereal packet and not mixed in?! ๐Ÿ˜ฉ๐Ÿฅ„or even at the bottom?!๐Ÿค” It can be super annoying when you want a breakfast of properly mixed cereal and get a bowl full of one ingredient. It also seems very strange that the larger things are at the top and haven’t sunk to the bottom๐Ÿคจ. But anyway, this can be solved by just shaking the box right?! โŒ Well actually the shaking of the cereal box on its travels into your food cupboard is probably what has caused this annoyance in the first place! When the cereal shakes, the larger nuts move and jump around forming gaps underneath them and the smaller muesli grains drop into these spaces. This means that the nuts eventually rise to the top of the pack and the muesli grains fall to the bottom. We call this the Brazil nut effect ๐Ÿฅœ. Cereals are granular materials (this means they are made up of grains!) and the Brazil nut effect can be seen with other granular materials too. Other examples of granular materials are sand, sugar, dessert sprinkles, coffee grains and snow. These materials have unusual properties – while one grain of sand is clearly a solid material, a group of loads of grains of sand can flow like a liquid through your fingers! If the change from being solid like to liquid like happens when you don’t want it to however, then it could cause big problems – like avalanches! ๐Ÿ—ป๐Ÿ˜จ Once again maths comes to the rescue ๐ŸŽ‰. Maths can be used to find safe ways of handling these granular materials by modelling how forces pass through each grain and the changes in flow when there are objects in the way. This maths has been used in the design of avalanche barriers to protect people.๐Ÿ˜Š โญ๏ธTry at Home activity๐Ÿ™Œ๐Ÿป: Add sugar and dessert sprinkles to a container and try to mix these together through shaking the container in different ways. What happens?!๐Ÿ‘€ย #appliedmathematicsย #physicsย #everydaymathย #mathsinlifeย #stemย #scienceeducationย #didyouknowย #materialsย #avalancheย #sandย #granularmaterialsย #womeninstemย #breakfastmathsย #scicomm

How maths can be used to give me a dog face ๐Ÿถ Snapchat filter algorithms!๐Ÿฆธ๐Ÿฝโ€โ™€๏ธ๐Ÿ‘ฐ๐Ÿป๐Ÿ‘ธ๐Ÿฝ๐ŸงŸโ€โ™‚๏ธ๐Ÿ‘ฉ๐Ÿปโ€๐Ÿš’๐Ÿ‘ฉ๐Ÿผโ€๐Ÿ”ฌ

How does snapchat know where to put the filters so that they are on the right part of your face and even stay on your face when youโ€™re moving around?!๐Ÿค” First your phone needs to decide which part of the image is your face! Pixels (or picture elements) are tiny squares of colour that make up the image. Snapchat uses a mathematical algorithm to repeat many searches through all the pixels of the image looking for regions of contrast between light and dark pixels. This is because there are common regions of every face that are lighter or darker than others (e.g. the middle of your forehead is lighter than the outside). Using this snapchat has found your face! But how does it know where your nose is so that it can replace it with a dog nose๐Ÿ‘ƒ ? Or where your lips are so they can be puckered up ๐Ÿ‘„ ?!…Well this is where statistics comes in. To do this, many people have manually told a computer where the outlines of their different facial features are – so many faces in fact that the average of this is used as a template on snapchat. This template is put over the image of your face and adjusted to your specific features through scalings, rotations and movements based on contrast in light and on where other features have been detected. The coordinates of your face and facial features are then remembered as a mask and tracked as you move your face to create the best pose ๐Ÿ•บ๐Ÿปย #appliedmathematicsย #mathsinlifeย #scienceiscoolย #mathsisfunย #keeplearningย #stemeducationย #womeninmathematicsย #snapchat๐Ÿ‘ปย #filtersย #faceย #dogfaceย #scicommย #spreadingtheword

Why do ambulance sirens sound different as they are driving away? ๐Ÿš‘

Sound travels in a wave starting from something that is vibrating and ending up in your ear๐Ÿ‘‚๐Ÿป. When the sound wave travels through the air it makes pockets of different air densities (how packed together the air molecules are in a given space). This corresponds to alternating regions of high and low air pressure (you might have heard these terms when listening to a weather forecast โ›ˆ ). The faster the air molecules vibrate, the faster each wave reaches your ear (higher frequency) and the higher the pitch we hear ๐ŸŽถ

So back to the ambulance sirens ๐Ÿš‘… When an ambulance is driving away from you, there is a longer distance between the air molecules that are close to the ambulance meaning that the vibration is slower between these molecules. Each wave will therefore take slightly longer to reach your ear and so you hear a progressively lower pitch. This is called the Doppler effect. We can use a simple mathematical equation to calculate the speed of the vibrations (frequency) we hear if we know the speed an ambulance is travelling away from us as well as the speed of the vibrations leaving the siren.๐Ÿ™Œ๐Ÿป This principle can also be used to detect speeding vehicles using radio waves fired from a police radar gun! ๐Ÿšจ โญ๏ธ Try at home sound waves activity: attach two pieces of string to one end of a slinky and tie the other ends of each string around one finger on each hand. Now listen to the difference in sound when dropping the slinky with those fingers in and out of your ears! Why does it sound different? ๐Ÿง
(Hint: think about how densely packed molecules are in solids compared to in the air)

Weird& Wonderful random maths fact ๐Ÿ‘€

Penguin eggs donโ€™t hatch unless they have been rotated and maths can help us understand why! ๐Ÿง ๐Ÿ™Œ๐Ÿป As we all know, eggs contain a round yellow yolk surrounded by a fluid egg white (called the albumen)๐Ÿณ The albumen contains important nutrients that the baby penguin needs to grow!
When a penguin lays an egg, the embryo develops at the top of the yolk. The density of the embryo compared to the yolk means that it always returns to the top of the yolk (since it is buoyant like a float in a swimming pool) . As well as this, the density of the yolk compared to the albumen means that the yolk (and therefore the embryo) always return to the very top of the egg! ๐Ÿฅš
When a penguin rotates their egg, the yolk and embryo slowly move back to the top of the egg. This creates a flow which mixes the nutrients in the albumen so that the embryo gets everything it needs to grow ๐Ÿ˜€

This mixing can be mathematically modelled using fluid dynamics!
It is important to know why penguins turn their eggs so that artificial incubators can be made to turn the eggs in the best way!

Weird& Wonderful random maths fact ๐Ÿ‘€

There is an angle above which an airplane will stall and fall ๐Ÿ˜ณ
But okay no need to panic, pilots correct this in most situations because they know their maths!
This important angle (called the angle of attack) is the angle between the imaginary line following the horizontal direction that the plane is flying in (or the direction that air is blowing against the front of the plane) and the imaginary line through the centre of the plane going from its tail to its nose. If this angle is too large, there will not be enough air flowing over the wings to keep the plane lifted causing a stall. Note that this stall is not to do with the engine like it is with cars!
But how come airplanes can do a loop the loop?! โœˆ๏ธ Well this angle of attack is never reached in a loop since the direction of both(!) of the imaginary lines mentioned above will change throughout the loop.
#appliedmathematicsย #mathsphysicsย #engineeringmathsย #stemย #scienceeducationย #scicommย #learnscienceย #mathsfunย #didyouknowย #aerodynamicsย #flightย #planeย #designย #funfactย #womeninscienceย #maths

Tortoise Turns ๐Ÿข

The shape of some tortoise shells means that if they fall on their back, they can turn back over all by themselves. These shells look a lot like the shape called a Gรถmbรถc, which is unique because it only has two resting places and one of these is nearly impossible to achieve (so that it always turns back to the same position). The mathematics behind this shape and itโ€™s properties can be used in a range of ways including in designing the shape of drones which often collide and get turned over!
#mathsinnatureย #appliedmathematicsย #whyweneedmathย #stemย #scicommย #learnscienceย #scienceeducationย #mathsisfunย #animalsย #shapesย #interestingfactsย #mathsinlife

Weird& Wonderful random maths fact ๐Ÿ‘€

In a room of 23 people there is a 50% chance that 2 people have the same birthday! ๐Ÿค”Whatโ€™s more is that in a room of 70 people this chance is 99.9%! ๐Ÿค”๐Ÿค” This might seem strange since there are only 23 people and 365 possible days to have a birthday. However if we think about pairs of people, 23 people gives 23*(23-1)/2 = 253 pairs which is more than half of 365. Using this and some basic probability we can calculate the percentage chance given any number of people๐Ÿฅณ

The understanding of this โ€˜birthday problemโ€™ has been used in computer hacking ๐Ÿ’ป


How does a zebra get its stripes and why should we care? ๐Ÿฆ“

We can see lots of patterns in nature: leopard spots, butterfly wing eyes and zebra stripes to name a few. While these all look pretty different, it turns out that there is a simple set of mathematical rules that can produce all these patterns. Alan Turing (the guy who created these rules) thought of cells as producing 2 chemicals that act very differently to each other. The rules show us that one of these chemicals spreads out faster than the other, leading to the slower chemicals all getting trapped in clumps. These clumps can be in different shapes like spots and stripes.

Knowing how these patterns are made is important for something called tissue engineering. This is because we can get cells outside of the body to organise themselves in the way they do naturally. These are then used to create tissues to replace damaged tissue eg. artificial skin for people with bad burns.


The Maths of Asthma ๐Ÿ‘ฉ๐Ÿผโ€โš•๏ธ

This is just one of the many medical applications of maths.
The airway can be thought of as a stretchy material that opens up as we breathe. When someone with asthma has an asthma attack, their airways contract/tighten making it difficult for them to catch their breathe. We can use maths to mimic this by using lots of tiny springs (for the stretchy airway material) that will stretch when you apply a force (breathing in) and then relax back to a resting length (breathing out). This information, as well as knowledge of interactions between different components of the airways, can be used to form mathematical/computational models which can be used to predict how an airway contracts. Methods like this have the potential to help us find new treatment options for severe asthmatics where current treatment does not work.
This work is being carried out in the CMMB research group at the University of Nottingham by Bindi Brook, Reuben Oโ€™dea, Hannah Pybus and myself, Sarah Brown. This photo was taken at Science in the Park 2019 ran by the British Science Association.



Hi! Iโ€™m Sarah (right) and I want to show you WHY your teachers taught you maths that you โ€œjust need to knowโ€. Everyone at some point in their school life thought ๐Ÿ’ญ whatโ€™s the point of this?!๐Ÿ’ญ but it turns out that maths is used in some pretty weird and wonderful ways that you might not expect, everywhere around us!
#maths #applications #whyarewetaughtthis #appliedmathematics #scicomm #outreach #wideningparticipation #womeninmathematics #mathsinmedicine #mathsinengineering #mathsinspace #mathsinnature #mathsinlife