How can you show geometrically that 3 < π < 4?

Approximating Pi was a favourite pastime of many ancient mathematicians, none more so than Archimedes. Using his polygon approximation method we can get whole number bounds of 3 and 4 for the universal constant, with only high-school level geometry.

This is the latest question in the I Love Mathematics series where I answer the questions sent in and voted for by YOU. To vote for the next question that you want answered next remember to ‘like’ my Facebook page here.

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Equations Stripped: Normal Distribution

Stripping back the most important equations in maths so that everyone can understand…

The Normal Distribution is one of the most important in the world of probability, modelling everything from height and weight to salaries and number of offspring. It is used by advertisers to better target their products and by pharmaceutical companies to test the success of new drugs. It seems to fit almost any set of data, which is what makes it SO incredibly important…

You can watch all of the Equations Stripped series here.

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BBC News – Maryam Mirzakhani’s Legacy

Live interview on BBC News about the legacy of Iranian Mathematician Maryam Mirzakhani who tragically passed away today (July 15th 2017). She was the first female winner of the Fields Medal – the mathematical equivalent of the Nobel Prize.

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Can a pill make you fitter?

These days it seems that we are always hearing about the latest ‘wonder pill’ that will help you to get fit – often with very little science to back it up. Well, this time things are a little different. Scientists at the Salk Institute in California have discovered a new pathway used by the body during exercise and are able to recreate its effects in mice by simply giving them a pill. The mice were able to run for a much longer period of time and gained less weight! I spoke to senior researcher Weiwei Fan to find out how it all works…

  • The process involves a protein called PPL-delta which during exercise turns up the genes that burn fat and turns down the genes that burn sugar.
  • Mice that were given a chemical to activate the PPL-delta protein over an 8-week period could run for about 270 minutes, whereas mice that were not on the drug could only run for about 160 minutes.
  • The activation of the protein not only increases endurance, but by burning fat instead of glucose it can also result in weight loss, making it a possible treatment for type 2 diabetes, obesity and fatty liver disease.
  • On a high-fat diet, the mice with the drug gained 50% less weight than those without, with the weight loss occurring almost entirely in fat rather than muscle.
  • The ultimate goal is to test the findings in humans once the current negative side effects of the drug are eliminated.

 

 

 

You can listen to the full interview for the Naked Scientists here.

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Funbers 11

A double-dose of double-digits with the number 11! It has quite the infamous history with the good – the Armistice on the 11th hour of the 11th day of the 11th month, the bad – September 11th and the attack on the Twin Towers, and the ugly – conspiracy theories including the so-called ‘fake’ moon landing of Apollo 11, making it an interesting number to say the least…

You can listen to all of the Funbers episodes from BBC Radio Cambridgeshire and BBC Radio Oxford here.

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Tom Rocks Maths Episode 06

Tom Rocks Maths is back on Oxide Radio with episode number 6! Featuring space travel, illegal numbers and the four (or should that be six?) Horsemen of the Apocalypse… Plus, music from Linkin Park, Four Year Strong and American Hi-Fi. This is maths, but not as you know it…

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World Cup 2018: The Perfect Penalty Kick

 

The 2018 World Cup in Russia kicks off today and so I bring you a special double-edition of Throwback Thursday looking at the science behind the perfect penalty kick… Fingers crossed the England players listen/read my website and we don’t lose to Germany in a penalty shootout (though let’s be honest we probably will).

Live interview with BBC Radio Cambridgeshire looking at the ‘unsaveable zone’ and the best way to mentally prepare for a penalty.

 

And if that wasn’t enough, here’s a full description of the ‘Penalty Kick Equation’…

For all of the footballers out there who have missed penalties recently, I thought I would explain the idea of the science behind the perfect penalty a little further, and in particular the maths equation that describes the movement of the ball. On the radio of course I couldn’t really describe the equation, so here it is:

Screen Shot 2017-06-05 at 10.09.22

If you’re not a mathematician it might look a little scary, but it’s really not too bad. The term on the left-hand side, D, gives the movement of the ball in the direction perpendicular to the direction in which the ball is kicked. In other words, how much the ball curves either left or right. This is what we want to know when a player is lining up to take a penalty, because knowing how much the ball will curl will tell us where it will end up. To work this out we need to input the variables of the system – basically use the information that we have about the kick and input it into the equation to get the result. It’s like one of those ‘function machines’ that teachers used to talk about at school: I input 4 into the ‘machine’ and it gives me 8, then I put in 5 and I get 10, what will happen if I input 6? The equation above works on the same idea, except we input a few different things and the result tells us how much the ball will curl.

So, what are the inputs on the right-hand side? The symbol p just represents the number 3.141… and it appears in the equation because footballs are round. Anytime we are using circles or spheres in maths, you can bet that p will pop up in the equations – it’s sort of its job. The ball itself is represented by R which gives the ball’s radius, i.e. how big it is, and the ball’s mass is given by m. We might expect that for a smaller ball or a lighter ball the amount it will curl will be different, so it is good to see these things are represented in the equation – sort of a sanity test if you will. The air that the ball is moving through is also important and this is represented by r, which is the density of the air. It will be pretty constant unless it’s a particularly humid or dry day.

Now, what else do you think might have an effect on how much the ball will curl? Well, surely it will depend on how hard the ball is kicked… correct. The velocity of the ball is given by v. The distance the ball has moved in the direction it is kicked is given by x, which is important as the ball will curl more over a long distance than it will if kicked only 1 metre from the goal. For a penalty this distance will be fixed at 12 yards or about 11m. The final variable is w – the angular velocity of the ball. This represents how fast the ball is spinning and you can think of it as how much ‘whip’ has been put on the ball by the player. Cristiano Ronaldo loves to hit them straight so w will be small, but for Beckham – aka the king of curl- w will be much larger. He did of course smash that one straight down the middle versus Argentina in 2002 though…

So there you have it. The maths equation that tells you how much a football will curl based on how hard you hit it and how much ‘whip’ you give it. Footballers often get a bad reputation for perhaps not being the brightest bunch, but every time they step up to take a free kick or a penalty they are pretty much doing this calculation in their head. Maybe they’re not quite so bad after all…

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A mathematicians age is but a number…

The third puzzle in the new feature from Tom Rocks Maths – check out the question below and send your answers to @tomrocksmaths on Twitter, Facebook, Instagram or via the contact form on my website. The answer to the last puzzle can be found here.

Can you place the (extremely) famous mathematicians below in order of the year that they were born, earliest first? Bonus points for telling me what they studied. Answer to be announced with the next puzzle – good luck!

birthdays_letters

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Funbers 10

We’ve finally reached double figures in the form of the number 10! The reason that ten is the first number with two digits is precisely because we count in base 10. Computers count in base two (0 and 1’s) and 7-tentacled aliens probably count in base seven…

You can listen to all of the Funbers episodes from BBC Radio Cambridgeshire and BBC Radio Oxford here.

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Why are fingerprints unique?

Question

Please put me out of my misery. How is it possible no one person’s finger prints are the same as another’s? How can one developing embryo possible know what pattern another developing embryo has chosen?

Answer

The movies say that if your fingerprints are found at the scene of the crime, you’re guilty. But does this notion hold up in the real world. Forensic scientist Professor Niamh Nic Daeid, put me through my paces at our very own virtual crime scene where, would you believe it, the murderer has left his fingerprints on the candlestick in the dining room.

  • In forensic science, we’re moving away from the notion that fingerprints can be considered as unique and instead talk about the comparison between fingerprints and finger marks.
  • Fingerprints are the records that are taken directly from a person’s finger by law enforcement and finger marks are what we take from crime scenes.
  • There are a range of characteristic patterns, called friction ridge patterns, which can be used to identify and compare fingerprints. They include: whirls, loops, arches and the location of ridge divisions.
  • Ridge patterns also occur on the palms of your hands and on your toes.
  • Fingerprints develop in the womb around the 10th week of pregnancy and are largely complete by the end of the fourth month.
  • Factors that influence their development include blood pressure, oxygen levels in the blood, the position adopted by the foetus in the womb, nutrition, hormone levels and the touching of fingers onto the sac and amniotic fluid, which means that even identical twins have different fingerprints!

You can listen to the full interview with the Naked Scientists here.

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Do antioxidants really keep you young?

As part of the Naked Scientists Mythconception series, I question my choice of new year resolution as I investigates the science behind the infamous ‘free-radicals’ and their sworn enemy, the all-conquering antioxidants…

Tom – We’re now well into the new year – how are those resolutions going? If, like me, you’ve decided to eat more healthily, maybe you’ve been stuffing yourself with antioxidants. They’re good for you… right? And they attack free radicals, those naughty things flying around in your body causing damage to your cells and making you age faster. At least that’s what we’re told by the so-called ‘health experts’. Let’s see what science has to say on the subject…

The story begins in 1945, when the wife of chemist Denham Harman suggested that he read an article in Ladies Home Journal entitled “Tomorrow you may be younger.” This sparked his interest in the process of aging and a few years later whilst working at the University of California, Berkeley, he proposed that ageing is caused by reactive molecules that build up in the body as by-products of your body’s natural processes and lead to cellular damage. These are what he called “free radicals.” Harman himself described his discovery as ‘a thought out of the blue.’

Scientists began to rally around the theory of free radical ageing and that antioxidants such as vitamin C and beta-carotene were able to neutralise them. The antioxidant boom occurred in the 1990’s with the word entering into the public domain and supplements being added to foods and taken as tablets. It wasn’t until the early 2000’s, however, that scientists began testing the theory and they encountered some interesting results. Two separate studies compared mice, which were genetically engineered to overproduce either free radicals or antioxidants, with normal mice and they saw no change in the life span in each case. Further studies in humans found antioxidant supplements negate the health promoting effects of exercise and may even lead to a higher chance of death.

The increase in life expectancy which is often attributed to antioxidants is, in fact, likely to be a by-product of a generally healthier lifestyle. People that take antioxidant supplements tend to be more health conscious in general and as a result, are likely to live longer.

The bottom line is that scientists are still unsure of the exact roles of free radicals and antioxidants in the body and more studies are required. Most researchers do agree, however, that free radicals cause cellular damage but this is not necessarily a bad thing. In many cases is seems to be a normal part of the body’s reaction to stress. We are certainly not being oxidised and therefore do not require antioxidants to save us from impending doom as the health experts would like us to believe.

Nonetheless, the global antioxidant market was worth 2.1 billion dollars in 2013 and is expected to continue to grow by a further billion by 2020. I’ll leave you with a quote from Professor David Gems from University College London, which sums it all up quite nicely – “It’s a massive racket. The reason the notion of oxidation and ageing hangs around is because it is perpetuated by people making money out of it.”

You can listen to the full interview with the Naked Scientists here.

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