Saturday, 28 February 2009

The Curious Sequence

A few days ago during my mathematical investigations, I discovered something of an anomaly. 

A normal Arithmetic or Geometric progression can be accurately represented by a formula which can be used to find the (n)th term of that progression. In this particular situation, I was working on the Fibonacci Sequence in which each term is the  sum of the previous two numbers.

1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89 .......................................

Now I thought it was a normal geometric progression and applied the formula to find out the (n)th term. First I divided successive terms to find a definite ratio between the numbers. To my surprise, there was none. I then tried to find the formula  thinking that it was an arithmetic progression. I tried to find the difference between the terms, and to my utter surprise found that each time I tried to find the constant difference between, a new Fibonacci Sequence is formed. Amazing, isn't it? 

Friday, 6 February 2009

The Recipe

The previous week I concocted a cake recipe for my English assignment. I was about to do what all other's would do: copy and paste the essentials from the internet and add their own touch. Then an idea struck me. I decided to do it impromptu, and just write down what came to my head. This was the the result.

1.Combine the butter, water, sugar, cocoa powder and chocolate together in a medium sized saucepan. 

2. Place over gentle heat. Bring to the boil whilst stirring. You need to stir until everything has dissolved to stop the mix from burning. After stirring 7 times clockwise, add 12 ml of pure honey of the finest quality. Continue stirring anti-clockwise for 13 minutes. Be careful that the mix does not boil over. Simmer gently for 5 minutes. After the third minute add three drops of vanilla essence and sandalwood extract.

3. Remove from the heat. Cover with a lid and leave to cool to room temperature. Heat the mixture gently again. Using a thermometer to measure the temperature, follow the next step while trying to keep the temperature constant at 37°C/98.6°F.  

4. Whisk in gently the flour and sodium bicarbonate into the liquid. Whisk 144 times. All lumps should have dissolved into the batter now. The batter should have achieved the viscosity of a mixture of corn-flour, soy-bean, sun-flower and olive oils.  

5. Pour batter into the prepared baking pan. Remember the baking pan must be lined with linseed oil mixed with unsalted butter. The batter should level naturally in 30 seconds. Tap the tin on the kitchen bench 8 times to remove any large air bubbles. 

6. Bake in a preheated oven set at 169.975oC (337.955°F) for 88 minutes. The top of the cake will crack and display a poison ivy pattern. Don’t worry the cracks will settle and be hidden when you turn the cake out of the tin. But Internal fissures will form, dividing the internal into three layers. This will not collapse as the mix is quite rigid. 

7. Remove from the oven. Leave in bright sunlight or a UV-Lamp for 11.5 minutes. The cake must display a colour of light brown tinged with golden patches.

8. During the 11.5 minutes melt 35 bars of 350g Toblerone chocolates in a vessel big enough to hold the cake but of small enough width to make the chocolate liquid level above the cake. Use a thermometer to keep the solution at 50°C. Gently drop the cake into the mix. It should sink completely within 45 seconds. 

9. To add to the flavor heat until the chocolate starts bubbling and within 5 minutes, add essence of strawberry and a teaspoon of Asafoetida powder. After 5 minutes the cake will have completely absorbed the chocolate and will sit in the container with a 0.8 mm covering of chocolate on the surface and two 1.3 cm layers inside.