Hallucii (A Penrose staircase)

Animation of Escher's Relativity

Who was M. C.Escher?

The Fibonacci numbers

Power of a power

Dividing powers

Multiplying powers...

To the power of.....

How do you manage with powers when the exponents are negative integers?

Powers

What is a power?

TIPS TO MAKE A GOOD PRESENTATION AT SCHOOL

STEP ONE: PREPARATION

1-. Plan your presentation, organizing your ideas.

2-. Think about the slides that you are going to prepare.

3-. Look for the photographs on the Internet.

4-. Copy and paste them on your slides and add a maximum of three short sentences in every slide.

5-. Look for some new words in the dictionary (Word reference is a good online dictionary)

6-. Don´t write too much text on the slides. The sentences are just a guide to help you.

7-. Use some colour and images, but not too much!

STEP TWO: REHEARSAL

1-. Try to rehearse your presentation, calculating the time you spend.

2-. Pay attention to pronunciation

3-. Be careful with grammar

STEP THREE: GIVE THE PRESENTATION

1-. Make eye contact with the students in your class.

2-. Try to keep your body still.

3-. Speak properly. Don´t talk too fast or too slow!

4-. Project your voice. Speak up so that everybody can hear you easily.

5-. Make your voice sound interesting.

6-. Stress the key words in the speech.

7-. Pause between ideas.

8-. And last, but most important: Don´t feel nervous.

More of Cristóbal Vila...

If you have enjoyed the previous video don't miss this one. You´ll find how the golden number and the Fibonacci sequence give shape to nature. Enjoy!

 

Cristobal Vila and M.C. Escher

Have you ever heard about M.C. Escher? No? Then it's about time! Please, have a look a this video. It´s inspired in his work. Every little detail is just a "little piece of beauty". Maths are intertwined with art in every image. So you will find allusions to the Seven Bridges of Königsberg problem or to Fermat´s theorem alongside paintings by: Francisco de Goya, Alberto Durero, Jan van Eyck, Johanes Vermeer, Leonardo Da Vinci....and more. Enjoy!

Lowest Common Denominator

Do you want to add fractions easily? Then, you should look for their lowest common denominator.

Factoring

Do you need a help with factoring? This video may help you

JOHN CARLIN SAVE THE PLANET(MONOLOGUE)

GENERATION STRESSED

YOUR NEW HOUSE CAN BE SUSTAINABLE TOO!

People might falsely believe that when they are building a house incorporating any sustainable solutions require additional costs and effort. It is actually the opposite. Some of the sustainable solutions require very little in any financing with comparison to the costs that need to be incurred anyways in a newly constructed building.



It is possible to save around 30% on the use of energy and water in a sustainable house. That is a case with any other sustainable solution, when it pays off to invest in environment friendly solution in every case.
Below there is list of sustainable solutions that can be applied in every house.

- Heat recovery system for the ventilation, heating and cooling.
- The use of geothermal heat pump for heating the house, allows for great savings on heating costs.
- It is common to use only floor heating as a heating option in energy efficient houses (no radiators).
- Use of low energy doors and windows (recommended triple glazed windows).
- Good insulation of the house (both walls, slabs and the roof!), exceed standard requirements, gives great savings in the long run on heating and cooling costs.

- Installation of kitchen hood with carcoal filter which does not keep the heat inside but retains it and reuses it in the house.
- Big openings – big windows but with shutters, allow for maximum light to get into the house but shutters are necessary protection against direct sunlight, and protect the interior from excessive heat. Glass roof or big roof windows that allow for a lot of light to come inside.
- The right positioning of the house, entertaining areas and rooms that are going to be used most – in the south.
- Use of natural and recycled materials for building the house – wood strongly recommended, especially from local areas where the need for long transportation is avoided. If concrete is to be used – find out about recycled concrete, possibly lower prices!

  
- Light roof and façade colors that allow not to overheat the exterior surfaces in summer, thus less energy is required to coll the house.
- Light control devices that are switching the lights off automatically in unoccupied spaces.
- LED lighting fixtures, that use very little energy and last forever.
- Electrical appliances (washing machine,dishwasher, fridge and so on) energy efficient.
- Use plants that do not require much watering and adapt easily.
- Limit areas with asphalt driveways and concrete pavements to a minimum, allowing for as much greenery as possible.

It is easy and cost effective to construct a sustainable house. While the natural resources are being save from an excessive exploitation, many dollars for utility bills are saved from our pockets . So do not hesitate. Be a part of the change.

THANKSGIVING DINNER´S CARBON FOOTPRINT

Thanksgiving Dinner's Carbon Footprint: A State-by-State Comparison

The environmental impact of your Thanksgiving dinner depends on where the meal is prepared.

Carnegie Mellon University researchers calculated the carbon footprint of a typical Thanksgiving feast – roasted turkey stuffed with sausage and apples, green bean casserole and pumpkin pie – for each state. The team based their calculations on the way the meal is cooked (gas versus electric range), the specific state’s predominant power source and how the food is produced in each area.

They found that dinners cooked in Maine and Vermont, states that rely mostly on renewable energy, emit the lowest amounts of carbon dioxide, a greenhouse gas that is tied to climate change. States that use coal power, such as Wyoming, West Virginia and Kentucky, have the highest carbon dioxide emissions.

"Food production – how the food is grown or raised – and meal preparation – how the food is cooked – both contribute to the carbon footprint. We broke our dinner down into its separate dishes, and then broke those down into the individual ingredients. For each ingredient, we tracked its carbon emissions from 'farm-to-fork.' Production and preparation both contribute about 50 pounds of carbon dioxide, but it varies from state to state and house to house," said Paul Fischbeck, professor of social and decisions sciences in the Dietrich College of Humanities and Social Sciences.

Further examination showed high variability among similar stove types in different states. For example, cooking a 16-pound turkey in an electric oven in coal-dependent Wyoming emits 32 pounds of carbon dioxide. In Maine, cooking the same turkey in the same oven but with electricity generated primarily from renewable energy releases less than three pounds of carbon dioxide.

Generally, using gas ranges to cook leaves a smaller footprint than electric ranges, but the team found that does not hold true for 11 states whose primary sources for electricity are renewables and nuclear power.

Traveling to celebrate Thanksgiving only worsens the problem.

THOUSANDS OF HIGH SCHOOL STUDENTS HAVE STAGED DEMONSTRATIONS IN CITIES ACROSS SPAIN TO PROTEST THE COUNTRY´S EDUCATION LAW, CHANGES IN THE DURATION OF UNIVERSITY DEGREES AND UNIVERSITY FEE HIKES. 

MADRID (AP) — Thousands of high school students have staged demonstrations in cities across Spain to protest over the country's education law, changes in the duration of university degrees and university fee hikes.

The protests Thursday were called by the Students Union, with the biggest marches taking place in Madrid, Barcelona and Valencia.

The demonstrations came at the end of a two-day strike by the students that had uneven support.

The education bill was brought in 2014 by the conservative Popular Party. Opposed by most other political parties and many teacher and parent groups, it increases the number of annual exams and reintroduced religion as a subject. The government claimed it was aimed at stemming Spain's school dropout rate.

Associated Press. USA

DRONES, BY MUSE

Perhaps you find this song relaxing after you have studied for your exams...

Killed by drones
My mother, my father,
My sister and my brother
My son and my daughter
Killed by drones
Our lives between
Your fingers and your thumb
Can you feel anything?
Are you dead inside?
Now you can kill
From the safety of your home
With drones
Amen

A SIGHT ON SPANISH EDUCATION

Overview

Education in Spain is compulsory from ages 6-16, and students have a choice of state-subsidized public schools, private schools and vocational training schools.

Spain has been arguably one of the hardest hit countries since the onset of the financial crisis. Since 2008 drastic austerity measures have been implemented across the country to slow the plunging Spanish economy, but it would seem that many of those implements have only served to worsen the economic situation, especially in the education sector.

Backwards austerity and a deteriorating education system

An education bill was recently introduced in May 2013 that aims to focus more intently on students' scores on standardized tests, which will determine funding per region (based on lower scores and higher drop-out rates). Students' scores will also serve as an early disqualifying factor for many students pursuing an education that fall below a certain level - those students will be separated and their vocational training determined for them. The bill affects religious education as well as language instruction in school. "The reform was imposed by the government despite the opposition of all other political parties and semi-autonomous regional governments, and it was approved by the parliament this fall in order to implement it in 2014’s school year." 

Unemployment in Spain was the highest in Europe at 23 per cent in 2012, and was above 50 per cent for people between 16-24 years old. That number has risen to nearly 27 per cent overall, with a 57 per cent rate for young adults in 2013. 


Investment in education was 21.9 per cent lower than previous years, whereas the cut on military expenditure is a mere eight per cent. Investment in ECE and primary education fell by 36.5 per cent, and higher education took the bulk of the cut, with a 62.5 per cent decrease in investment.

TWENTY ONE PILOTS

I wish I found some better sounds 
No one's ever heard
I wish I had a better voice 
That sang some better words
I wish I found some chords 
In an order that is new
I wish I didn't have to rhyme 
Every time I sang
I was told when I get older 
All my fears would shrink
But now I'm insecure 
And I care what people think

My name's "Blurryface" 
And I care what you think
My name's "Blurryface" 
And I care what you think

Wish we could turn back time
To the good old days
When our momma sang us to sleep 
But now we're stressed out
(bis)

Sometimes a certain smell 
Will take me back to when I was young
How come? 
I'm never able to identify 
Where it's coming from
I'd make a candle out of it 
If I ever found it
Try to sell it? never sell out of it
I'd probably only sell one
It'd be to my brother
Because we have the same nose
Same clothes homegrown 
A stone's throw 
From a creek we used to roam
But it would remind us of when nothing really mattered
Out of student loans and treehouse homes 
We all would take the latter

My name's "Blurryface" 
And I care what you think
My name's "Blurryface" 
And I care what you think

Wish we could turn back time
To the good old days
When our momma sang us to sleep 
But now we're stressed out
(bis)

We used to play pretend
Give each other different names
We would build a rocket ship 
And then we'd fly it far away
Used to dream of outer space 
But now they're laughing at our face
Saying, "wake up, you need to make money"

Wish we could turn back time
To the good old days
When our momma sang us to sleep 
But now we're stressed out
(bis)

We used to play pretend
We used to play pretend
Money
We used to play pretend
wake up, you need the money
(bis)

We used to play pretend
Give each other different names
We would build a rocket ship 
And then we'd fly it far away
Used to dream of outer space 
But now they're laughing at our face
Saying, "wake up, you need to make money"

Twenty One Pilots - Stressed out

GENERATION STRESSED

NEWS FOR STUDENTS

HOW TO SPEAK SO THAT PEOPLE WANT TO LISTEN

Here you are they videos and lyrics of the songs that you are working with in the Music classes. We hope you enjoy them, learn them by heart, and try to get some useful new words for your English classes. 

TOO MUCH LOVE WILL KILL YOU, BY QUEEN

I'm just the pieces of the man I used to be
Too many bitter tears are raining down on me
I'm far away from home
And I've been facing this alone
For much too long
Oh, I feel like no-one ever told the truth to me
About growing up and what a struggle it would be
In my tangled state of mind
I've been looking back to find
Where I went wrong

Too much love will kill you
If you can't make up your mind
Torn between the lover
And the love you leave behind
You're headed for disaster
'Cause you never read the signs
Too much love will kill you - every time

I'm just the shadow of the man I used to be
And it seems like there's no way out of this for me
I used to bring you sunshine
Now all I ever do is bring you down
Oh, how would it be if you were standing in my shoes
Can't you see that it's impossible to choose
No there's no making sense of it
Every way I go I'm bound to lose
Oh yes

Too much love will kill you
Just as sure as none at all
It'll drain the power that's in you
Make you plead and scream and crawl
And the pain will make you crazy
You're the victim of your crime
Too much love will kill you every time

SHOW MUST GO ON, BY QUEEN

Empty spaces, what are we living for
Abandoned places, I guess we know the score
On and on, does anybody know what we are looking for
Another hero, another mindless crime
Behind the curtain, in the pantomime
Hold the line, does anybody want to take it anymore
The show must go on
The show must go on, yeah
Inside my heart is breaking
My make-up may be flaking
But my smile still stays on

Whatever happens, I'll leave it all to chance
Another heartache, another failed romance
On and on, does anybody know what we are living for?
I guess I'm learning (I'm learning learning learning)
I must be warmer now
I'll soon be turning (turning turning turning)
Round the corner now
Outside the dawn is breaking
But inside in the dark I'm aching to be free
The show must go on
The show must go on, yeah yeah
Ooh, inside my heart is breaking
My make-up may be flaking
But my smile still stays on

Yeah yeah, whoa wo oh oh

My soul is painted like the wings of butterflies
Fairy tales of yesterday will grow but never die
I can fly, my friends
The show must go on (go on, go on, go on) yeah yeah
The show must go on (go on, go on, go on)
I'll face it with a grin
I'm never giving in
On, with the show

 

VIRGIN AMERICA SAFETY VIDEO

I've got some safety tips that you ought to know And trust me it's something that you want to hear So honey zip you're lips and enjoy the show

Before we move into the stratosphere So won't you buckle seatbelt Put it on tight And keep you're oh in that chair till we turn off that light Turn you're electrical devices off as fast as you can And whatever you do don't make me ask you again So tonight get ready to fly Cause we're gonna live it on up in the sky Virgin America knows all the places you want to be Fly away with me Fly away with me yeh For the point zero zero one percent of you that has never operated a seatbelt before Really I mean it works like this Insert the metal end into the buckle until it clicks And pull on the loose end to tighten Making sure it fits low and tight across you're lap There you go To open lift on the the top of the buckle Now remember seatbelts should be fastened whenever you're seated Just in case of unexpected turbulence or weather conditions Personal electronic devices should be properly stoed during taxi take off and landing Laptops should be placed inside carry ons or under the seat Not in setback pockets or loose on the seat next to you Nice try

PHOTOGRAPH, BY ED SHEERAN

Loving can hurt, loving can hurt sometimes

But it's the only thing that I know
When it gets hard, you know it can get hard sometimes
It is the only thing that makes us feel alive

We keep this love in a photograph
We made these memories for ourselves
Where our eyes are never closing
Hearts are never broken
And time's forever frozen still

So you can keep me
Inside the pocket of your ripped jeans
Holding me closer 'til our eyes meet
You won't ever be alone, wait for me to come home

Loving can heal, loving can mend your soul
And it's the only thing that I know, know
I swear it will get easier,
Remember that with every piece of you
Hm, and it´s the only thing we take with us when we die

Hm, we keep this love in this photograph
We made these memories for ourselves
Where our eyes are never closing
Hearts were never broken
And time's forever frozen still

So you can keep me
Inside the pocket of your ripped jeans
Holding me closer 'til our eyes meet
You won't ever be alone

And if you hurt me
That´s okay baby, only words bleed
Inside these pages you just hold me
And I won't ever let you go
Wait for me to come home
Wait for me to come home
Wait for me to come home
Wait for me to come home1

You can fit me
Inside the necklace you got when you were sixteen
Next to your heartbeat where I should be
Keep it deep within your soul

And if you hurt me
Well, that's okay baby, only words bleed
Inside these pages you just hold me
And I won't ever let you go

When I'm away, I will remember how you kissed me
Under the lamppost back on Sixth street
Hearing you whisper through the phone
"Wait for me to come home."

GANG OF RYTHM, BY WALK THE EARTH

I got this old guitar
The strings are rusty
But it's all I need
Bring in the kick drum
It can back the beat
Let's gather round and sing a song
I got a shaker too
The kinds of sound
That wants to make you move
Bring in the uke
It will complete the groove
Let's gather round and sing a song

There's no worries on the earth tonight
We're all walkin' off the world tonight

Come on now everyone yeah
Come on now everyone
We're like a locomotive
Under the big hot sun
We're chained to the gang of rhythm
The song is never done
Come on now everyone yeah
Come on now everyone
Come on everyone

We got this melody
Bring in the harmony like CSNY
To write a tune you know will never die
Let's gather round and sing a song

There's no worries on the earth tonight
We're all walkin' off the world tonight

Come on now everyone yeah
Come on now everyone
We're like a locomotive
Under the big hot sun
We're chained to the gang of rhythm
The song is never done
Come on now everyone yeah
Come on now everyone
Come on everyone

And when the night is done
These chains will hold us strong
The chords will carry on
Long after we're gone oh oh

There's no worries on the earth tonight
We're all walkin' off the world tonight

Come on now everyone yeah
Come now everyone
We're like like a locomotive
Under the big hot sun

Come on now everyone yeah
Come on now everyone
We're like a locomotive
Under the big hot sun
We're chained to the gang of rhythm
The song is never done
Come on now everyone yeah
Come on now everyone
Come on everyone

We got this melody
Come on everyone
Bring in the harmony
Come on everyone

I got this old guitar
The strings are rusty
But it's all I need

THINGS, BY BOBBY DARIN

Ev'ry night I sit here by my window (window)
Starin' at the lonely avenue (avenue)
Watching lovers holdin' hands 'n' laughin' (laughin')
And thinkin' 'bout the things we used to do

Chorus
(Thinkin' of things) Like a walk in the park
(Things) Like a kiss in the dark
(Things) Like a sailboat ride
(Yeah-yeah) What about the night we cried?
Things like a lover's vow
Things that we don't do now
Thinkin' 'bout the things we used to do

Memories are all I have to cling to (cling to)
And heartaches are the friends I'm talkin' to (talkin' to)
When I'm not thinkin' of-a just how much I love you (love you)
Well, I'm-a thinkin' 'bout the things we used to do

Chorus

I still can hear the jukebox softly playin' (playin')
And the face I see each day belongs to you (belongs to you)
Though there's not a single sound and there's nobody else around
Well, it's-a just me thinkin' of the things we used to do

Chorus

And the heartaches are the friends I'm talkin' to
Ya got me thinkin' 'bout the things we used to do

Fade
Starin' at the lonely avenue

BASIC STRUCTURE IN ESSAYS

SOME TRICKS TO ENGAGE THE READER WITH YOUR ESSAY STRUCTURE: 

INTRODUCTION, BODY AND CONCLUSION

WRITING A DESCRIPTION

WATCH THIS VIDEO AND IT WILL HELP YOU WITH YOUR WRITING

WRITING A NARRATIVE

USEFUL ADVICE TO WRITE YOUR ESSAYS

USEFUL LINKERS

YOU CAN IMPROVE YOUR WRITING BY USING THESE LINKERS AND CONNECTORS

LINKERS OF ADDITION

In addition As well as Also Too Furthermore Moreover Apart from In addition to Besides

- Ideas are often linked by and. In a list, you put a comma between each item, but not before and.

"We discussed training, education and the budget."

- Also is used to add an extra idea or emphasis.

"We also spoke about marketing."

- You can use also with not only to give emphasis.

"We are concerned not only by the costs, but also by the competition."

- We don't usually start a sentence with also. If you want to start a sentence with a phrase that means also, you can use In addition, or In addition to this…

- As well as can be used at the beginning or the middle of a sentence.

"As well as the costs, we are concerned by the competition."
"We are interested in costs as well as the competition."

- Too goes either at the end of the sentence, or after the subject and means as well.

"They were concerned too."
"I, too, was concerned."

- Apart from and besides are often used to mean as well as, or in addition to.

"Apart from Rover, we are the largest sports car manufacturer."
"Besides Rover, we are the largest sports car manufacturer."

- Moreover and furthermore add extra information to the point you are making.

"Marketing plans give us an idea of the potential market. Moreover, they tell us about the competition."