Interesting Maths Question

I saw this interesting maths question on TV.

PQRS is a rectangle with PQ = 15 units, QR = 6 units and it is divided into 4 smaller rectangles by two lines, TU and VW. T is a point on PS, U is a point on QR, V is a point on PQ and W is a point on RS. X is the intersection point between TU and VW. If the area of triangle SXW is 4 sq units and area of triangle XVQ is 16 sq units, find the area of rectangle XURW.

Here is my solution:

Let WR = x and RU = y.

This means that
(XURW) = xy
SW = (15 - x)
UQ = (6 - y)

(SXW) = 4
==> (TXWS) = 8
==> (15 - x)y = 8 ---- (1)

(XVQ) = 16
==> (VQUX) = 32
==> x(6 - y) = 32 ---- (2)

From (1), y = 8 / (15 - x) ---- (3)
Sub (3) into (2)
==> x(6 - 8 / (15 - x)) = 32
==> 6x (15 - x) - 8x = 32 (15 - x)
==> x^2 - 19x + 80 = 0
==> x = (19 +- sqrt(41)) / 2 ---- (4)

Sub (4) into (3)
==> y = (11 +- sqrt(41)) / 5 --- (5)

(4)*(5) ==> xy = 25 +- 3* sqrt(41)
==> (XURW) = 25 +- 3* sqrt(41) sq units

Both solutions for the area of rectangle XURW satisfy the consistency check that 0 < x < 15 and 0 < y < 6. Note that the assumption that S, X and Q are collinear is not true.

Check out a related link here

Afternote: By replacing the hardcoded values with variables using (TXWS) = A, (VQUX) = B, PQ = w, QR = h and k = wh - (A + B),

I found that (XURW) = (k +- sqrt(k^2 - 4AB)) / 2

Control

I watched this at GV Plaza as part of the European Union Film Festival. As I made my way up the escalator, I saw gigantic banners of "The Legends of Zorro" and they look very good, especially the one with Catherine Zeta Jones!

The story is about the everyday life of a group of ticket controllers. They have to deal with many different types of passengers who refuse to co-operate. It made me realise how tough the job of the ticket controller could be. I also like the ambience in the subway and the cool soundtrack. The girl in the bear costume look quite cute too!

Internet Movie Database Link

The Brothers Grimm

The story is about the encounters of the brothers grimm who were witch hunters. A difficult task was assigned to them and it was to find missing girls who were taken away from the village to an enchanted forest with a deserted castle.

Monica Belluci who acted as the queen in the castle looked quite pretty! Liked the funny scene with the toad in a belly up position! Didn't like the scenes with the soldiers as I think they should be trimmed off to make the show more compact. Had fun identifying fairytales like "The Little Red Riding Hood", "Hansel and Gretel", "Rapunzel", "Snow White", "Sleeping Beauty" and many others that were incorporated into the show seamlessly!

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When The Rain Lifts

The story is about a few days in the life of an unemployed samurai and his wife during the rainy season. They were initially staying in an inn before the husband got invited to be a fencing master at a castle.

The samurai is very skilful! I liked the way he dodges his opponent easily! A little disappointed with the lack of action, passion and suspense like in "The Incident" or "The Tragedy of W", but the film is still enjoyable as a quiet little piece peppered with a dash of humour!

Internet Movie Database Link

The Incident

The story is about a shipyard worker being tried for killing a woman who was his girlfriend's sister. The whole film is centered around the court, similar to that in 12 Angry Men and Rashomon.

My favorite film so far at the Japanese Film Festival followed closely by TTOW! Liked the exciting court room scenes and how the film slowly describes in-depth about each character! Very well written script! I also like the complex relationship among the chracters!

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Castle of Sand

The story is about detectives solving a murder case of an old man who had been a model policeman.

As in the previous film, I am amazed at how the detective can find out what happened from seemingly unconnected clues! The flashback about the son and the father is quite well done! The soundtrack is nice too! One thing that does not look quite right is the pianist doubling up as the conductor at the same time.

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Zero Focus

The story is about a newly wed wife searching for her husband who went missing during a business trip. Many secrets were revealed during the process!

For the first few minutes, I was distracted by the mole on the actress's face but I soon forgot about it as more clues pop up and the mystery deepens! The scenery at the countryside is very nice, especially that on the cliff! The rich man's wife looks quite fierce though!

Internet Movie Database Link

The Tragedy of W

My first film at the Japanese Film Festival. The Japanese Association of Singapore is showing a number of films for free at its auditorium and this is one of them. The story is about how an aspiring actress got the leading role of a play named "The Tragedy of W" through an unexpected turn of events.

Very similar to All About Eve that won the 1951 Best Picture Academy Awards but with more detailed explanation on the training and auditioning process. Well written script that shows how real life parallels the stage play! The actress looks quite pretty too!

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Be With Me

Went to watch the film as Ezann Lee is acting in it! There are three subplots in the film and they share a common theme: a longing for our loved ones. "Meant To Be" is about a lonely old provision shopkeeper. "Finding Love" is about a middle aged security guard who secretly admires someone working in the same building as he does. "So In Love" is about how the relationship between two teenage girls changes over time.

BWM is inspired by an extra-ordinary woman, Theresa Chan, who is both blind and deaf but still manages to lead an independent life. She is also the glue that joins the three stories together. Her story reminds me of The Land of Silence and Darkness which I saw not long ago.

I like the nice piano soundtrack and the minimal use of dialogue to convey the message! Ezann Lee and the security guard acted very well! Samantha looks quite pretty too! Some minus points are too many close-ups and information overload in the subtitles. Highly recommended!

Internet Movie Database Link
Review with nice movie stills!

The Three Colors Trilogy

The Three Colors Trilogy is a series of films by Polish director Krzysztof Kieslowski based on the three colors of the French flag: blue, white and red. The colors represent liberty, equality and fraternity respectively. "Blue" is about a young woman re-discovering herself, "White" is about a an ex-husband seeking revenge on his wife and "Red" is about a beautiful model's encounter with a stranger.

The nice DVD boxset that I bought at HMV comes with lots of special features! The cover looks very pretty too! I just started to watch the special features in "Blue" and there are many interviews with the lead actress Juliette Binoche, film critics and the director's friends.

Saw "Blue" a few years ago at Alliance Francaise and I was impressed by the visual effects with the use of colors, the in-depth character development and the small little details that link the three films together. The interviews gave me a better insight into how the different film techniques are used to tell the story more effectively! The DVD is rated M18 though, so you can't watch it if you are under 18.

Blue: Internet Movie Database Link
White: Internet Movie Database Link
Red: Internet Movie Database Link

The Bow

Saw this at the Korean film festival in Orchard Cineleisure. The story is about a 60 year old man and a 16 year old girl living on a boat together. The old man is waiting for the girl to reach 17 years old to marry her. Meanwhile, outsiders would pay to come on board to fish and stay a few days. The relationship between the girl and the old man changes when a college guy gets on board the ship.

This is a quiet film where the two lead characters hardly speak at all but the expressions on their faces say a lot about what they feel. I think it is interesting how the bow is used both as a weapon and a musical instrument! The same bow is used by the old man to shoot at people who harass the girl, as well as to play music when he is bored. The way the old man helps his customers tell their fortune is also very innovative!

The director Kim Ki Duk has taken ideas from his previous films and put it in this one. The setting is similar to The Isle where people fish on a quite lake, the same actress acted in Samaritan Girl, the quiet couple reminds me of 3 Iron and scenes where people peep through the window reminds me of Bad Guy. I think KKD has toned his film down quite a bit in terms of sex and violence since his early days. TI and BG had a R21 rating, SG was M18, 3I and TB both has an NC16 rating.

The ending is very well done and I like the surprise twist at the end where the arrow fell from the sky and something happened!

Internet Movie Database Link
Korean Film Review

March of the Penguins

An interesting French documentary about the Emperor Penguins living in the polar regions. Not sure whether is it North or South pole though. I guess it is the North pole as I didn't see any polar bears around.

What makes this different from regular documentaries is the use of songs and first person narration to tell the story. This allows us to feel closer to the penguins rather than cold facts and figures. Didn't realise that the penguins have to travel so much during their life! They look like elegant businessmen in suits when they walk, cool surf boarders when they slide on their stomachs and great athletes when they swim and leap out of the water! The scenery looks quite pretty too!

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Dude, Where's My Car?

Chanced upon this little gem when I was channel surfing. The story is about what happened when two friends, Jesse and Chester, woke up and found that their car was missing. They soon discover that this is not a simple case of car theft and that they are involved in something very much bigger.

Jesse and Chester have many strange encounters as they try to recover their car. I like the interesting people that they meet and the funny gags that play on words! The film reminds me of The Discrete Charm of the Bourgeoisie when they show how sadistic the officer at the car pound is and the several dream sequences by one of the main leads. The way they repeat their dialogue also reminds me of how Kevin Bacon lamented to his psychologist in The Woodsman that their conversation is like a merry-go-round.

The finale is very well done! I am very impressed by how the two friends use both their wits and brawn to handle a super-emergency situation! The large scale special effects is visually stunning too!

Internet Movie Database Link

The Woodsman

The film is about how an ex-offender adjusts back to society despite constant temptation to return back to his evil ways and prejudice from other co-workers.

Kevin Bacon plays the lead character in TW. We see him working quietly by himself in the lumber yard, having therapy with his psychologist and watching the activities at the school across his home. A female co-worker and a police sergeant would sometimes visit him to see how he is doing.

Great acting by Kevin Bacon! His facial expression allows the audience feel his struggles to lead a "normal" life. It reminds me of his performance in "Hollow Man" where he acted as a man who turned invisible in an experiment and was tempted to do things that he would normally not do.

The conversations with the psychologist and the police sergeant are quite interesting too! Also liked the touching scene with Kevin Bacon sitting on the bench in the park talking to someone towards the end of the film!

Afternote: Check out http://www.yellowribbon.org.sg/ that describes events that aim to help ex-offenders. I saw the ads when I was taking the bus home.

Internet Movie Database Link

Art Museum By The Zoo

Missed a large part of the show as I thought Central was showing it another day when I saw the stills of "The Way Home" in the newspaper. In actual fact, the two Korean films were showing on the same 9pm time slot: the former on Central and the latter on Channel U. Incidentally, I was browsing http://us.imdb.com and found that both films are by the same director!

AMBTZ looked quite interesting from the few scenes that I saw! The male and female leads collaborated to write a story that talks about how a girl working at the art museum met a vet at the zoo. Didn't quite catch the details as I was watching "The Apprentice" at the same time but the leads do have the right chemistry together! The female lead, Shim Eun-Ha also acted in "Christmas In August" that is another film that I enjoyed.

Art Museum By the Zoo: IMDB Link
Art Museum By The Zoo: Korean Film Review

Christmas In August: IMDB Link
Christmas In August: Korean Film Review

Man with a Movie Camera

A 1929 silent film documentary made by Russian director Dziga Vertov. The story is about a man who carries the movie camera around and films scenes from many interesting places such as coal mines, factories, railway stations, salons, a lady's house and the city. I like the soundtrack that fit nicely to the story and the special effects!

The editing is very well done to acheive the special effects! We see the director standing on top of the camera in one scene and appearing within a cup in another. The use of freeze frame shows the facial expression of selected individuals, slow motion shows atheletes in action and fast motion shows the trams, horses and people rushing about in the town!

I especially like the scene where they show the operator frantically connecting the lines from one node to another node! I feel that the trams, horses and people move a bit too slow even though it is already in fast motion. Guess I am too used to the speed of automobiles racing on the highway to appreciate it.

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The Land of Silence and Darkness

This 1971 documentary by German director, Werner Herzog, is about the lives of people who are both blind and deaf. The story is told through a middle aged woman who became blind and deaf during her teens. She actively organises outings for people who have similar disabilities.

Interesting to learn how they communicate through braille drawn on the hand and fingers of the receiver! The film shows a couple of their adventures: flying on a plane, touching the cactus (ouch!), feeding the elephant and carrying a monkey. We learn that these people can lead a normal life despite their disabilities.

The film also shows the plight of the minority who are abandoned at homes and how difficult it is to teach children who are born deaf and blind. I realised how fortunate we are. It also made me empathise better with Kelvin Tan, the visually challenged contestant of project Superstar.

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The Discrete Charm of the Bourgeoisie

An interesting film about a group of friends trying to have a meal together but some strange incident (both real and imaginary) would always occur to prevent it from happening. It is a political satire about people with great wealth and high social standing. The film won the Academy Award for Best Foreign Picture in 1972.

The director, Luis Bunuel, is very good at filming dream sequences! I think he is influenced by his friend, Salvador Dali, who is a surrealist painter. My favorite parts of the film are those where the characters recall a dream that they had before. One soldier dreamt about an unforgettable incident during his childhood and another dreamt about his old acquaintances. Both are very well done!

The rest of the film does not really have a main storyline but still manages to capture the attention of the audience as many strange things happen. There is even a lesson on how to prepare a martini! The scene where the ambassador shot at something on the ground through the window and the one where a girl wore the hat of a certain famous person came across as the most memorable for me.

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Scrabylon / Word Wars

Bought these two Scrabble documentaries during the National Day holiday and they are pretty interesting!

Scrabylon is about the 2001 World Scrabble Championship at Las Vegas. It explains a little bit about the history of Scrabble and why some of the players like the game so much. It is a straight forward documentary that shows the rational aspect of the game like learning the wordlist, having a good situation awareness of the board and calmly analysing the game after it has ended.

Word Wars on the other hand revolves its story around four players and how they prepare for the US Scrabble Nationals in San Diego. It reveals the emotional aspect of the game like the effect of Scrabble on the player's personal life, the carmaraderie among the players and the player's facial expression during the game itself. I especially like the the short and sharp video clip on the rules of Scrabble and the use of computer animation to virtually re-arrange the tiles on the screen itself! Had fun trying to guess the word before the time is up!

Watching the tiles fly around on the screen reminds me of a game in "Discovery Kids" on the Discovery channel where they show a zoomed-in view of a particular thing while giving many hints on what that is, one at a time. A time slider bar is shown at the side and it slowly slides from a score of fifty to zero. The objective is to guess what that particular thing is as quickly as possible. I always had fun playing that game too!

Picked up the following interesting anagram combinations from Word Wars. See if you can guess what they are without using LexPert!!

RIGHT + LANE = ?
LAS + VEGAS = ?
SAN + DIEGO = ?

Learnt the following words from Word Wars:
WADI (n) a dry riverbed
ALIENOR (n) one who transfers property
JERRID (n) a blunt javelin
CLABBERS (n) a complex variation of Scrabble
TENTER (v) to stretch on a frame
GENTIAN (n) a flowering plant
DATELINE (n) the origin of a news story
NONLIFE (n) the absence of life
ESTUARY (n) an inlet to a river
BEDSORE (n) a sore caused by a prolonged stay in bed
OBLIQUE (adj) slanted
AZURE (n) a blue color
DOURINE (n) a disease of horses
VODUN (n) religion of the west indies
EGESTING (v) discharging from the body
VARNA (n) a Hindu social class
EXORDIA (n, pl) beginnings
SYLVITE (n) an ore of potassium
DJIN (n) a genie
RETSINA (n) a Greek liqueur
REVELRY (n) noisy merrymaking
ARENOSE (adj) sandy
QUAI (n) a wharf
FRUGAL (adj) thrifty
TWA (n) two
OUTBOXED (vb) surpassed in boxing
INARABLE (adj) unsuitable for farming
INDOLE (n) a chemical compound

Scrabylon: IMDB Link
Word Wars: IMDB Link

The Wayward Cloud

The film reminds me of a Guinness record breaking attempt shown on TV. The objective is to smash as many watermelons as possible with your forehead in one minute and the record now stands at 16!

The story is about how people live after the city is hit by drought. To quench their thirst, they buy mineral waters and water melons. The lead actor, Lee Kang Sheng and actress, Chen Hsiang Chi stay in the same apartment and they start seeing each other when the actress recognizes the actor as a former acquaintance.

There is not much dialogue except for several interesting musical numbers interspersed throughout the film. I like the sound of the clogs on the ground when the lead actress walk about and her brilliant acting performance as a lonely girl searching for someone to care for her!

Internet Movie Database Link