Qu.34) The Fibonacci numbers Fn are defined by the recurrence relation
Fn = Fn−1 + Fn−2, for n≥2
And F0 = 0 and F1 = 1. Prove for every integer n≥0, that
Fn = αn−βn√5
α = 1+√5-2 and β = 1−√5-2
I look down at the exam paper. A simple question to have to answer. I turn the page of the answer booklet, the question already memorised in my head, and start to write down the half a page of working required to answer the question.
Something moving in the corner of my eye makes me look up. A group of four guards are carrying a large metal crate across the snowy path in front of the classroom. They appear to be struggling with the weight of the load. It doesn’t interest me so I turn back to complete the paper. I finish the question and turn over the page to the penultimate one. Again it is simple to answer.
There’s a loud crash from outside. The guards have dropped the crate and are arguing amongst themselves. One of them has dropped his gun and is hopping on the spot, holding his hand.
“Ruddy hell,” Mutters Dr Stark from the front of the room, sat behind his desk. He neatly orders the stack of paper that he was reading and stands up. “I’ll be back in a moment, Mars. Keep working on your paper. You have fifteen minutes left.” He runs his left hand through his thinning ginger hair and leaves the room. I turn back to the final question of my mathematics paper. The exam doesn’t count for anything. Nor have the other seventeen that I have already completed this week. They just want to show the results to the board so that funding for the laboratory continues. I jot down the answer to the last question, 8πα, and fold up the answer and question booklet. My pen and pencil go back into the front pouch of my bag and I stand up. I pick up and place the papers on Dr Stark’s desk and then return to my seat. Dr Stark strolls over to the guards. They stop arguing immediately and line up in front of him. He doesn’t have any official power over them yet few people argue with Dr Stark. He steps up and inspects the crate. It doesn’t have appeared to have been damaged in the drop.
He takes a torch from the closest guard and peers between the narrow gaps in the bars. All around the box he moves, staring intently into the crate. When his back is facing me he jumps back slightly. The guards do the same even though they can’t see what Dr Stark is looking at. The crate begins to rock slightly. There must be a live creature inside. It is probably another Chimpanzee for use in their tests. The box keeps on rocking, the movement steadily becoming more vigorous. Dr Stark points his arms at the guards and then towards the metal box. I can hear the muffled sound of his voice shouting at the guards through the double glazing of the classroom. I can’t understand a word that he is saying but he isn’t happy. He is demonstrating the common physical characteristics of a person who is very angry. Or upset. But I think that he is angry.
And that is not a good thing. The guards often shy away from Dr Stark and I’ve overheard rumours of an incident at his previous job. I have two choices; leave since I have finished the paper, or wait until he comes back. Both have consequences but I am drawn to the later. Staying allows me to watch the situation outside from a safe distance. I pick up my papers and return to my desk. I open them, pretending to be working whilst I keep an eye on the situation outside.
There’s a loud bang from outside. The box has stopped moving but the guards around it are retreating slightly, their guns raised. Even Dr Stark is stepping backwards, his body blocking the majority of the crate from my eyesight. He then takes a step to his left, moving towards the closest guard. The metal crate is in full view. And hairy arm disappears back into the box through a fist sized hole. It was no Chimpanzee or monkey’s arm. If anything it belonged to a human. But no normal human or primate could punch a hole through a thick iron cage.
Dr Stark steps up again this time with a gun in hand. He blocks my view again but appears to point the gun through the hole made by the creature inside. Two quick shots sound from the gun. Whatever the creature was it is now dead. Dr Stark hands the gun back to the guard and immediately starts to order them back into action. The guards fall back into formation and lift the crate up. They begin to carry it off as Julia Sanders marches over from her office. The snow is kicked up into the air in front of her as she heads towards Dr Stark in her high heeled shoes. Another set of guards walk past carry another crate. Dr Stark watches them carefully before turning and talking to his boss.
Their conversation is brief before she turns and points at me. Dr Stark turns in unison and they both stare straight at me. I react quickly and stare straight back down at my paper. I don’t dare to look up but I know that they have seen me watching the scenario outside unfold. Nothing much happened but I feel like I am in trouble for watching. I take out my pen and pencil and check my answers to the paper. There’s no point though, they are all correct. I won’t have made a mistake.
I hear the door of the classroom open and look up. Dr Stark moves into the room with a small cut on his forehead.
“Sir, you are bleeding on your forehead.” His face flickers before he smiles and pulls a handkerchief out of his trouser pocket. He reaches up and touches the oozing wound. “Bloody monkeys. Have you finished the paper, Mars?” I nod.
“Then bring it over and be on your way,” I put away my pen and pencil and take the paper over towards him. He snatches it out of my hand and slouches into his desk chair. I leave the room.
Been a while since I have been here but I have been busy at work with various things, mostly starting my one year apprenticeship, however my book has slowly been progressing and I wanted to share some of it with you for some more feedback and constructive criticism.
Due to the way my next few years seem to be planned out I really want to finish this book completely by summer 2015 before I head off to the chaos of University. So I am making it the most important thing in my life now and any help would be greatly appreciated.
For those of you who read my first draft of Ch 1 it differs a lot so if you prefer one to the other let me know.
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