Some Math and Surtsey

In math I have recently been evaluating sequences in recursive form. 

$Here\; is\; problem\; that\; I\; copied\; off\; Khan$Academy ( and how to solve it ):

$f$ is a function that describes a sequence, and is therefore defined over the positive integers. This is the recursive definition of the function:

$\qquad f(n) = \begin{cases} -3 & \text{if } n=1 \\ -5 \cdot f(n\!-\!1) -7 & \text{if } n > 1.\end{cases}$

Generate the first four terms of the sequence.

$f(1)=$
$f(2)=$
$f(3)=$
$f(4)=$

so f(1)=-3 ( as the table tells us )

and then f(2)=-5*f(2-1)-7=-5*f(1)-7=-5*-3-7=15-7=8

and f(3)=-5*8-7=-40-7=-47

finally f(4)=-5*-47-7=228

I learned about a volcanic island today, named Surtsey, which is off the coast of southern Iceland. The name of the island came from a fire giant from Norse mythology, named Surtr ( Iceland was populated by Norsemen before 1000 AD , and has Norse culture ). It started erupting above surface in November 1964, and has been dormant since about 1966. The first sighting of it erupting was made by a cook on a nearby ship. Iceland claimed it and it is part of Iceland. It has been used as a scientific researching area, by volcanologists ( volcano geologists ) and biologists. The volcanologists studied the eruption and how the island fought the erosion caused by the sea ( among other things ). The biologists studied the founder populations of living organisms that populated the island coming from the outside. The sea continually eroded the Island, but the Eruptions added more and more rock to the island so it grew . After 3 or so years though , the eruptions abated ( and then stopped )  and the erosion damage started making an impact. The Island is getting smaller every year, but once the sea gets to the hard strong ( almost ) non-erodible rock at the core of the Island, the erosion rate will decrease. The living organisms the biologists studied include insects, plants ( including non vascular and vascular ) and birds. The insects and plants were first, and then the birds came, and the way they are connected in a food web is amazing. The Insects eat the plants, then the birds come and the insects provide food for them. There were at first few plant species, but when the birds came and fertilized the soil more , more species were able to survive. Also dead birds provided food for carnivorous insects and decomposers. The Island became protected and only scientists were allowed to go on shore. Everyone who goes on shore now is checked to make sure they are not bringing any new seeds to the island. 

Europe Adventure

We recently got back from an Adventure in Europe. We first packed, then we drove to a bus station. At the bus station we parked and got on the bus to Boston. We got off at the airport and discovered someone had taken our bag. We went to terminal E and took a Aer Lingus flight to Dublin that lasted about 5 hrs & 20 minutes. We did not have that one bag, but the bus company was searching for it. In Dublin we took a taxi to a fishing village , saw a castle there and ate at a cafe. We had about 4 hr layover so then we took another taxi back to Dublin airport. The currency in Ireland was Euro's but they drove on the left side of the road. So they had a bit of English culture left from the time Britain ruled Ireland. The taxi drivers did not really like England and one played a Irish rebel song when we asked him his favorite Irish music. We took another Aer Lingus flight from terminal 2 to Inverness Scotland. That flight was only an hour and a half. In Inverness we got a Mercedes rental car that turned off when you stopped ! We drove towards Skye after we got some food from a market. There were sheep and green hills everywhere!

 We stopped on our way and hiked up a hill and had a picnic on it. There were many small rivulets running through the hills too. We saw plenty of sheep on our way to Skye. We stopped at some castles like Eileen Donan and Urqhart

.  We also went to a town called Strontian, where strontium was discovered. In Skye we slept in a cottage, and explored many places, including Portree ( the capital ), and the fairy springs                  

next to the Cullens ( a mountain range ). Then we went down to Stirling, and saw Stirling Castle. After this we went down to Edinburgh and the surrounding towns. We saw Edinburgh Castle

and went to church in DalKeith. We also went through a flower field ( around North Berwick )                        

. We hiked up a The North Berwick Law ( or just the Berwick Law ), in North Berwick , it is a hill that has a whale's Jawbone ( now a replica , added in 2008, after one rotted away , and was removed in 2005 )  on the top. It also has ruins of an Iron age hill fort and military bases of many wars, including the Napoleonic and WWII. I got lost on it but, We found each other later. After this we had a Flight booked for London, but when we stopped on our way to the Airport , Our Sister's lip got slashed on the concrete. We went to the airport , and they told us that we should get it stitched, ( by the way the medical agent there was not very helpful ) But they couldn't do it, and there was a hospital 7 miles away or so. So we went to St Johns hospital and waited forever in the emergency room. Then after some more waiting in a patient's room, there came a facial surgeon and he stitched our sisters lip up. We had missed our flight from Edinburgh airport, and drove around, after getting some food at Tesco's, to find a hotel to sleep for the night. We went to hotel one hotel, they said no, then another ( that they recommended to us ), that said no , and another ( that they recommended to us ) , that said NO. But , finally we found one that said yes! and we slept there during the night. There was a deal if you book flights the day before them , before midnight, then they are cheaper. Our dad booked our flight to London , like 2 minutes before Midnight. We slept there that night, and then had a Breakfast there , for they had breakfast served there. That day we flew to London, we had lost some time, so we did not go to Oxford. But we took a bus tour of London, and saw Big Ben's tower              

, Parliament , and other buildings. We then flew to Bergerac, France, and then drove to Beynac.

There we slept in an old ( about medieval ) stone cottage of the hill that had the castle. The Cottage was refurbished on the inside for modern needs. We explored much of the Dordogne

, and some of the castles around it, I got my Sword in one of the Castles.

After this we drove to Paris in a rental car we had gotten in Bergerac airport. We lost a wallet at one of the tolls, but finally, after some 6 hours, we made it to Paris. In Paris we explored

, and saw Notre Dame

 ( there was a statue of Charlemagne near it, and many pigeons  ) , The Louvre and the Eiffel Tower

( I touched the base of this one ). From here we flew to Dublin, and after a 2 hour layover ( that was delayed some more ), we flew to Boston. It was great to be home, and we had a great time in Europe.

Recent learning and other things

Recent learning

Recent reading
Recently I have read the Hero's guide series. Book's 1,2 and 3. Here is some stuff about book 1: This series is made around making fun of Prince charming and some fairy tails. It changes them and combines them into an crazy and funny series. This book introduces the characters and tells us the real names of the prince's charming. Liam,Gustav,Duncan and Frederic. Liam is the Prince charming from Sleeping beauty, Gustav from Rapunzel, Duncan from snow white and Frederic from Cinderella.      

I also have been reading the Rangers apprentice series. Its a series placed in medieval fantasy land of Araluen, Scandia Teutland, Gallica , Temujai , Celtia and more.  These countries and people's probably are based on real modern day countries. Araluen probably being England ( I don't see any name reason here but i think it is england beacuse of the Longbows and some other things ) , Scandia most likely being Scandinavia( you can see the oblivious name reason here), Teutlandt probably Germany ( the name reason is probably from the Teutonic knights and Deutschland ,see how it ends with land? ), Gallica might be France ( Here it is most likely because of the Gauls )and Temujai ( I can not really see the name reason here besides it is Asian. But I think it is the mongols because the guy who started the Temujai  is called something close to Temuchin the name of Genghis khan and the leaders are called Shan close to Khan  ) the Mongols or the Huns or combined. But most likely the Mongols. The Main Character is will a young orphan at the starting and then finds out his Dad died bravely and strongly on the battle field. He lived in Castle Redmont as a ward. Wards lived In castle Redmont until they were 15 or so and then they could be chosen to be an apprentice to one of the craftmasters. Will had ward comrades: Horace, Jenny, Alyss and George. Horace got to be a Warrior apprentice , Jenny a cook apprentice, Alyss a Diplomat apprentice and George a scribe apprentice. But will , none of the official craftmasters wanted him. If no one would accept you as an apprentice you would have to go work as a farmer. But Will got excepted by Halt the fief's ( a place under control of a Baron and with his knights protected the Farmer. There were other Fief's and they all listened to the King of Arualen. This was where Will lived. The king's name was Duncan. ) Ranger. Rangers were a mystery to ordinary low ranking People. These people thought the did black magic. But what the Kings Rangers were and actually did was not his. The Rangers were an Elite scout team that were expert archers and knife throwers. They could spy on the enemy and see what they were doing. They were experts at moving without being seen and at tracking. Rangers were Rangers. They wore the Oak leaf to show that they were actual rangers. Bronze meant Apprentice and silver meant senior. Halt was a highly esteemed ranger he had lead the army when they beat Morgarath and evil villain. But he still existed. Anyway Will spent hour after hour day after day training with is Bow and knives. He also practiced Camouflage ( Rangers wore Ranger clocks , green and gray things ) keeping unseen, tracking and reading maps. Once Will , Halt, Horace and some Knights went Boar hunting. There were 2 boars but the y thought there was only one. After the first one had been killed the second dashed at Will. Will dived , Rolled , jumped and shot arrows at it. But this boar could not be killed unless an arrow hit his heart. Will missed every time and was just about to be killed when Halt shot it right in the heart killing it. After this Will went on to Kill a Kalkalra a (fearsome enemy that was only scared of fire . These Kalkara were enlisted by Morgarath the evil lord who goes on to almost beat the Araluen army with his army of Wargals. Also fearsome enemies ( their weakness being Calvary ) , but not as strong as the kalkara. These Kalkara were assassins . The hypnotized anyone close to them and then could kill them. ) by shooting a flaming arrow at it burning it. Will also burned a bridge that was vital to the Araluen win at the Plains of Uthal.

Below you can read some of the actual History.

Recent science
I have been learning a lot about chemistry. You can see half of some of the stuff I learned here here and here. I will be coming up with the second half soon with stuff about Biochemistry, pH ,acids, bases Nuclear chemistry and much more. I also have been learning some cool facts at Joppa flatts , like how to tell a green crab from an Asian shore crab,Sea stars have a brain at each foot, Sea urchins and sea stars are both Echinoderms (phylum) and are related and Moon snails eat other smaller snails called periwinkles by wrapping themselves around them, dropping acid , drilling a hole through them and sucking them up! Another cool fact is that sea stars eat with their stomachs. You can read more about Joppa flats in the Other things/joppa flats section of this post.

Fast fact! 
Saturn had the most moons, At least 25. While Venus has no moons.

Recent History and Recent Geography
History
I have not been doing much on History recently besides the world cup. I am going to publish the blog: Some History ( I changed World History since 1300 to this ), that includes The Huns,Vikings,Goths and Mongols; Early medieval Japan,Korea and China;Summary of the Story of the World 1,2,3 and 4 and more! Here are some sneak peaks.

Huns,Vikings,Goths and Mongols
here is a link to the downfall of Rome, I wrote last year, it has some information on the Huns and Goths.
 Huns:
 In the late 300's the Huns attacked Europe from western Asia, east of Europe. Eastern Europeans/Romans were terrified of them. The Huns raided and destroyed settlements. To make themselves even scarier than they were they slashed their faces( ouch ), And wore weird ragged clothes. The Huns were nomads ( people who moved from place to place always setting and taking down tents. They had no home. ) and expert horsemen.

#2 Rich leaders of the Huns wore jewelry to show they were rich. One jewelry item was the fibula , The Fibula was like a pin , it was usually made out of gold and had gems in them.

Vikings: 
The Vikings started in 793 and ended in 1066 ( this period is called the viking age ). The vikings came from Scandinavia, a region in Northern Europe that includes Norway,Denmark,Sweden and Finland ( not to many vikings in Finland though ). The Vikings were fearsome war crazy raiders. They were also explores( expert navigators) and amazing shipbuilders. The vikings traded,Explored,Raided and Colonized many places

Raiding and wars
The first viking raid ( outside Scandinavia ) was against England. England was raided by Vikings from Denmark. They raided a monastery called  St. Cuthbert's monastery off the eastern coast of England. The day it happened was the start of the viking age 7/19/793 AD.

Peaceful life and Exploration
 Back at home in Scandinavia they led mostly non warlike lives ( but they did fight and raid each other ever so often ). They lived in houses with large central rooms made out of wood. They had a hole in the roof for the smoke from a fire, that burned inside the house (  to give light for these houses rarely had windows. It was probably also used for cooking) to go out.


Goths:



Mongols:


Early medieval Japan,Korea and China

Around the 500's Japan was divided into many different clans. One of these Clans , the Yamato Clan, was stronger than the others. The Yamato clan wanted to conquer the other clans and rule Japan.



Geography
I have been doing postcrossing. In this you send and receive postcards to and from other countries. I have recieved 7 ( Germany, Australia, Canada, Russia, Finland and other places) post cards and have sent 5(Russia,China, Germany, USA, Belarus/Russia ). I also have been doing stack the states and stack the countries. I think we have beat them. I made a flag map some months ago, you can see it here.
Recent Math
I have been doing Khan academy for math here is an update for all the math I have been doing.

I put a progresses report here and it keeps going away

I am 3 skills away from mastering 5th grade. The recently added a lot of things for early math. This is preschool,kindergarten,1st grade and 2nd grade. You see though it shows that I have not mastered some of it. I don't think I should bother with things I already know and should keep learning( and believe me I know early math ).



Other Things


Joppa Flats
I recently joined the Joppa flatts staff as a volunteer. Here I clean caterpillar cages, Help people with crafts, Talk to them and help them hold creatures in the touch tank and other things. I like it there, I usually stay from around 9:00  to around  3:00. Then I come home. Joppa flats teaches you all about Sea creatures and many other things in science.



How to train your dragon 2
This was a great  movie minus a few things


Soccer



Recent art and Music

Sources: Barbarians, The story of the world voulume 4 and 3, Wikipedia, Myself, Khan academy and Rangers Apprentice and Brainpop