Archive for November, 2013

At first glance, you might be curious as to what this post is about. In that case, I would recommend learning the difference between ‘fallacies’ and ‘phalluses’. Dirty buggers. No, today won’t be spent talking about the male appendage – rather, some maths! Don’t sound too excited…

Yes, this post will be all about mathematical fallacies: these are ‘mistakes’ in mathematical proofs. However, the difference between a genuine mistake in a proof and a fallacy is that a fallacy will often lead to absurd results and conclusions that may seem flawless. Only when we examine the proof itself do we find the fallacy. So, today I’m going to show you some famous-ish fallacies that I find particularly interesting.

1. Fun With Fractions

Fractions is probably the part of maths that most people hate. Personally, I don’t mind them, but to some people they are the spawn of Satan. After all, there are so many rules to follow: “when can I divide?”; “Which fraction do I flip to divide?”; “Why am I even doing this?!” Many many questions to ponder. Below is a little example of some of the misunderstandings that go on when people deal with fractions. Now be warned, this is NOT how you simplify fractions. It just so happens that it works for this one example. Try it: type into your calculator ’16/64′ and it’ll simplify to 1/4. To all you non-mathematicians, sit back and marvel at how delightfully simple this fallacy is; to all you mathematicians, I challenge you to find another example where this kind of error works.

“But…erm…it’s right…”

2. Imaginary Numbers

To many people, the thought of imaginary numbers is ridiculous. In fact, I would wager that a lot of people wish that all numbers were imaginary and thus irrelevant. But I’m afraid that these imaginary numbers are far from irrelevant. The main thing to be aware of in terms of imaginary numbers is that the square root of -1 is called ‘i‘. Now, using that knowledge, behold as I prove that 1 = -1.

I feel a disturbance in the Mathematical Force…

At first glance this proof seems completely logical, however, there is an ever-so-tiny thing wrong with it. Now I could explain why this proof makes no sense, but it’s far more fun to let you work it out for yourselves. So, if you think you know the answer, please leave a comment!

3. MORE Imaginary Numbers

Wow, people just cannot get enough imaginary numbers, eh? This little fallacy is in the same style as the previous one. This time, the proof is showing how the square root of -1 is just 1 (which we know is impossible – remember I said it was that funny little number called ‘i‘). So, have a bash at this one!

Handy Hint: consider the fourth roots of 1…

“This is madness!”

4. Tricky trigonometry

‘SOHCAHTOA!’ – No, that’s not a made-up Japanese word, but a way of remembering the 3 trigonometric formulas! (‘Sine, Opposite, Hypotenuse, Cosine, Adjacent, Hypotenuse, Tangent, Opposite, Adjacent’) Ah, such fun! Trigonometry is the study of triangles and the relationships between their angles and sides. You can do lots with good ol’ trig: calculate angles, calculate sides, erm…calculate…other things too. Anyway, this fallacy proves that 0 = 2! Doesn’t that sound dramatic? Well, you’re probably aware of the fallacious proof that 1 = 2 (done so by dividing by zero – a huuuuuge no-no in maths) but this proof uses trigonometry! Have a look-see at this bad boy!

Handy Hint: it’s very close to number 3 in the list…

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Screw the maths, just look how neat my handwriting looks!

So, I’m afraid our mathematical journey must come to an end! We’ve had some ups, some downs, but most importantly – we’ve learnt some maths. I appreciate that this entire post may have gone over some people’s heads, but hey, sometimes I like to do maths.

Till next time,

Tom.

Here’s another guest post about one of the most famous superheroes on the planet. No, it’s not me, it’s….Superman! Today’s article was written by Samuel Rutherford – a TV and movie blogger. Enjoy!

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Superman has had a long history of appearing on TV and in movies ever since he left the realm of comic books. The DC Comics superhero has been the subject of many different big and small screen adaptations, leaving an impression on popular culture over the decades. Here, we take a look at the Man of Steel’s Hollywood and televisual history, both good and bad. The hero from the planet Krypton has starred in a huge list of media, but here are some of the highlights.

The Adventures of Superman (1951-58)

George Reeves' 1950's Superman

Superman’s first television show was titled ‘The Adventures of Superman’ and first aired in America in 1951. It was based on the comic book which had first appeared in 1938, created by Jerry Siegel and Joe Shuster. George Reeves played the role of Clark Kent/Superman and the show was initially filmed in black and white, although the series upgraded to colour in 1954. Episodes followed a similar plotline, whereby criminals and gangsters would cause trouble and only Superman would be able to save the day. The show started off quite gritty and violent, but eventually mellowed to become more comic fantasy. By today’s standards it seems very dated and camp.

Superman Movies (1978-87)

Christopher Reeve as Superman in the original movie quadrilogy

The first full length Superman movie debuted in 1978 and told the origin story of the famous hero on the big screen. Superman: The Movie was a box office smash and featured what would now be considered primitive special effects, but at the time it was pretty ground breaking. Christopher Reeve played Clark Kent in this adaptation. The first Superman movie was so popular with audiences that three sequels were made, also starring Reeve. Although the quality declined in the later movies, the films have had a great impact on popular culture, with many shows such as Family Guy having parodied iconic scenes and characters from them. The Superman movies were also the first superhero films to hit the cinemas, even before Batman.

Superman: The Animated Series (1996-2000)

Superman From The 90's Animated Series

Although there have been dozens of cartoon series of Superman, this late 90’s adaptation has been one of the most critically acclaimed. Following the success of Batman’s cartoon revival in Batman: The Animated Series, a Superman series soon followed, which aired for 4 seasons. The show was highly praised for its mature, adult orientated interpretation of the Superman comics that was faithful to the source material and pleased fans of all ages. Today it is still revered as one of the best Superman cartoons of all time.

Smallville (2001-2011)

Tom Welling as Clark Kent in Smallville

This spin-off TV series has come to be one of the longest running and popular adaptations of Superman, airing for 10 seasons and consisting of over 200 episodes. Based on a young Clark Kent (played by Tom Welling), before he has become Superman, it follows his time as a young man growing up in the country town of Smallville. The show’s initial premise was to focus on the teen drama of a young man growing up with extraordinary powers but in a humble setting. Over the course of the show, events led up to Kent eventually moving to Metropolis and later seasons were based around his early career at The Daily Planet before becoming Superman. Smallville was consistently popular, particularly with a teen audience, but audiences declined towards the latter seasons. Its ten year run on air meant it has become the longest running Superhero TV show ever made.

Man of Steel (2013)

Latest Superman Film, Man of Steel

With his Batman trilogy wrapped up, Christopher Nolan set his sights on Superman next for another gritty reboot of a popular superhero. Man of Steel was produced by Nolan but the director’s seat belonged to Zack Snyder, and the aim was to bring back credibility to the Superman brand after the lacklustre 2006 film, Superman Returns. Henry Cavill stars as Superman in this film, which is notably darker than previous big screen adaptations of the hero and focuses more on his alien origins. The movie has received mixed reviews from critics, however, with the expectations that Man of Steel would be as well-loved as the new Batman trilogy not quite being met. It has still been a box office smash in terms of ticket sales though.

These are just a few examples of Superman’s appearance in movies and on TV over the years, with plenty of other movies, cartoons and shows to explore. Superman has a had a mixed reception on our screens and a tougher time being loved outside of his comic book universe than Batman, but its still interesting to see how producers have interpreted his iconic tale.