on the road

(Reblogged from fairielphotos)

icelandicphoto:

Hveravellir is an oasis in the center of the Icelandic wilderness, in between Langjokull (Iceland’s second largest glacier) and Hofsjokull (Iceland’s third largest glacier).

Hveravellir means “Hot spring - fields” due to the number of geothermal hot springs and steam vents. Besides the great unspoiled mountain view and big vistas, it has a great natural geothermal pool.

(Reblogged from icelandicphoto)

flitterling:

Volcanic Lightning, Eyjafjallajökull, Iceland, by Terje Sørgjerd

(Reblogged from flitterling)

tatterhood:

Save the viking goats!!!

Johanna Thorvaldsdóttir’s Icelandic goat farm (Háafell) is facing foreclosure in September, resulting in the entire goat flock being butchered - unless enough funds are raised to save it!

There are less than 820 Icelandic goats in the entire world - they are an endangered species. Almost half of them will be lost if this farm is not saved. I visited Háafell 2 years ago and every goat I draw is rooted in this place. Any little bit helps :)

(Reblogged from tatterhood)

tatterhood:

Save the viking goats!!!

Johanna Thorvaldsdóttir’s Icelandic goat farm (Háafell) is facing foreclosure in September, resulting in the entire goat flock being butchered - unless enough funds are raised to save it!

There are less than 820 Icelandic goats in the entire world - they are an endangered species. Almost half of them will be lost if this farm is not saved. I visited Háafell 2 years ago and every goat I draw is rooted in this place. Any little bit helps :)

(Reblogged from tatterhood)
(Reblogged from magicalnaturetour)
(Reblogged from dutchster)

(Source: modddy)

(Reblogged from the-greater-masturbator)

trigonometry-is-my-bitch:

All planets, and Pluto, aligned.

(Reblogged from trigonometry-is-my-bitch)
trigonometry-is-my-bitch:

Things to know about Fibonacci and his Numbers -(by request)
Leonardo Pisano Bigollo (known as Fibonacci, and also Leonardo of Pisa, Leonardo Pisano, Leonardo Bonacci, Leonardo Fibonacci) —was an Italian mathematician, considered by some “the most talented Western mathematician of the Middle Ages.”
Fibonacci is best known for the spreading of the Hindu–Arabic numeral system which we use today in modern times - In his Liber Abaci (1202), Fibonacci introduced the modus Indorum (meaning method of the Indians), today known as Arabic numerals - which include the numbers 0 - 9 and was one of the earliest numerical systems to use zero as a place holder.  The book also advocated place value in early hindu-arabic numerals.

^ modern Arabic numerals
The Fibonacci sequence
The Fibonacci numbers were introduced in his Liber Abaci which posed, and solved a problem involving the growth of a population of rabbits based on idealized assumptions.
The solution, generation by generation, was a sequence of numbers later known as Fibonacci numbers. The number sequence was known to Indian mathematicians as early as the 6th century, but it was Fibonacci’s Liber Abaci that introduced it to the West.
the Fibonacci sequence is widely known for its interesting properties. the one you may be most familiar with is that every term is the addition of the previous two terms:

for example, the Fibonacci sequence is represented here in this famous pattern.
Your sequence begins with a square with side length of 1. Imagine this is one rabbit - if you pair one rabbit with no rabbits you will have no offspring. we then add a partner rabbit, so you have 1 and 1 paired together. 
the number of offspring they produce is the sum of the previous two generation’s population, in this case because we start with only 1 and 1 rabbits we get 2 in the next generation.
at this point your sequence looks like 1,1,2,
your next population of offspring continues the same rule - the sum of the previous two populations of the rabbit generation. So in this case where X is our fourth population in the next generation (1,1,2,X). X is the sum of 1 and 2 - the previous two populations.
The Rule is Xn = Xn-1 + Xn-2
so we now have the sequence 1,1,2,3
and the 1,1,2,3,5
and the sequence can carry on to infinity:
1,1,2,3,5,8,13,21,34,55,89,144,233,377,610,987,1597,2584…
The characteristics of the Fibonacci sequence is commonly found in sunflower seeds and seashells as well as many other forms of nature, Art and Architecture.



The Golden Ratio
The Fibonacci numbers were first expressed in terms of the Golden ratio by Daniel Bernoulli  in 1724.
The Golden ratio is one of the few Famous Mathematical constants along with e, √2, and π. It is an Irrational number.
In mathematics, two quantities are in the golden ratio if their ratio is the same as the ratio of their sum to the larger of the two quantities.

If we continue divide a term in the Fibonacci sequence by its preceding term we eventually approach the Golden ratio designated by the Greek numeral ϕ (phi, lowercase φ):
1/1= 1.000
2/1= 2.000
3/2= 1.500
5/3= 1.333
…..
55/34= 1.617
89/55=  1.618
etc.
the Golden ratio is approximated to the decimal 1.618033988
with this we can show that each Fibonacci number can be written in terms of Phi.

^ The golden ratio fits coherently with the Fibonacci pattern (where the curve is the Golden ratio and the squares are the Fibonacci numbers.)


^ Fibonacci numbers can be found in many other mathematical discoveries, as it is the one of the most naturally occurring sequences in Mathematics. Fibonacci numbers can be found in the Pascal triangle when you add the numbers diagonally.
Finding the Nth term in the Fibonacci sequence
The Formula to find the Nth term in the Fibonacci sequence can be calculated with the Golden ratio:

sources - [1] [2]

trigonometry-is-my-bitch:

Things to know about Fibonacci and his Numbers -(by request)

Leonardo Pisano Bigollo (known as Fibonacci, and also Leonardo of Pisa, Leonardo Pisano, Leonardo Bonacci, Leonardo Fibonacci) —was an Italian mathematician, considered by some “the most talented Western mathematician of the Middle Ages.”

Fibonacci is best known for the spreading of the Hindu–Arabic numeral system which we use today in modern times - In his Liber Abaci (1202), Fibonacci introduced the modus Indorum (meaning method of the Indians), today known as Arabic numerals - which include the numbers 0 - 9 and was one of the earliest numerical systems to use zero as a place holder.  The book also advocated place value in early hindu-arabic numerals.

^ modern Arabic numerals

The Fibonacci sequence

The Fibonacci numbers were introduced in his Liber Abaci which posed, and solved a problem involving the growth of a population of rabbits based on idealized assumptions.

The solution, generation by generation, was a sequence of numbers later known as Fibonacci numbers. The number sequence was known to Indian mathematicians as early as the 6th century, but it was Fibonacci’s Liber Abaci that introduced it to the West.

the Fibonacci sequence is widely known for its interesting properties. the one you may be most familiar with is that every term is the addition of the previous two terms:

for example, the Fibonacci sequence is represented here in this famous pattern.

Your sequence begins with a square with side length of 1. Imagine this is one rabbit - if you pair one rabbit with no rabbits you will have no offspring. we then add a partner rabbit, so you have 1 and 1 paired together. 

the number of offspring they produce is the sum of the previous two generation’s population, in this case because we start with only 1 and 1 rabbits we get 2 in the next generation.

at this point your sequence looks like 1,1,2,

your next population of offspring continues the same rule - the sum of the previous two populations of the rabbit generation. So in this case where X is our fourth population in the next generation (1,1,2,X). X is the sum of 1 and 2 - the previous two populations.

The Rule is Xn = Xn-1 + Xn-2

so we now have the sequence 1,1,2,3

and the 1,1,2,3,5

and the sequence can carry on to infinity:

1,1,2,3,5,8,13,21,34,55,89,144,233,377,610,987,1597,2584…

The characteristics of the Fibonacci sequence is commonly found in sunflower seeds and seashells as well as many other forms of nature, Art and Architecture.

The Golden Ratio

The Fibonacci numbers were first expressed in terms of the Golden ratio by Daniel Bernoulli  in 1724.

The Golden ratio is one of the few Famous Mathematical constants along with e, √2, and π. It is an Irrational number.

In mathematics, two quantities are in the golden ratio if their ratio is the same as the ratio of their sum to the larger of the two quantities.

If we continue divide a term in the Fibonacci sequence by its preceding term we eventually approach the Golden ratio designated by the Greek numeral ϕ (phi, lowercase φ):

1/1= 1.000

2/1= 2.000

3/2= 1.500

5/3= 1.333

…..

55/34= 1.617

89/55=  1.618

etc.

the Golden ratio is approximated to the decimal 1.618033988

with this we can show that each Fibonacci number can be written in terms of Phi.

^ The golden ratio fits coherently with the Fibonacci pattern (where the curve is the Golden ratio and the squares are the Fibonacci numbers.)

^ Fibonacci numbers can be found in many other mathematical discoveries, as it is the one of the most naturally occurring sequences in Mathematics. Fibonacci numbers can be found in the Pascal triangle when you add the numbers diagonally.

Finding the Nth term in the Fibonacci sequence

The Formula to find the Nth term in the Fibonacci sequence can be calculated with the Golden ratio:

sources - [1] [2]

(Reblogged from trigonometry-is-my-bitch)

futurescope:

Solar energy that doesn’t block the view

A team of researchers at Michigan State University has developed a new type of solar concentrator that when placed over a window creates solar energy while allowing people to actually see through the window. It is called a transparent luminescent solar concentrator and can be used on buildings, cell phones and any other device that has a clear surface. And, according to Richard Lunt of MSU’s College of Engineering, the key word is “transparent.”

[read more at MSU] [paper] [picture credit: Yimu Zhao]

(Reblogged from trigonometry-is-my-bitch)

trigonometry-is-my-bitch:

standingfor:

joachimmurat:

trigonometry-is-my-bitch:

A Wooden simulation of a water droplet as it impacts a body of water.

[Source]

This is very calming to watch.

Can we take a moment to appreciate trigonometry-is-my-bitch ‘s URL?

oh you :)

(Reblogged from trigonometry-is-my-bitch)

thenewenlightenmentage:

Are White Holes Real?

Sailors have their krakens and their sea serpents. Physicists have white holes: cosmic creatures that straddle the line between tall tale and reality. Yet to be seen in the wild, white holes may be only mathematical monsters. But new research suggests that, if a speculative theory called loop quantum gravity is right, white holes could be real—and we might have already observed them.

A white whole is, roughly speaking, the opposite of a black hole. “A black hole is a place where you can go in but you can never escape; a white hole is a place where you can leave but you can never go back,” says Caltech physicist Sean Carroll. “Otherwise, [both share] exactly the same mathematics, exactly the same geometry.” That boils down to a few essential features: a singularity, where mass is squeezed into a point of infinite density, and an event horizon, the invisible “point of no return” first described mathematically by the German physicist Karl Schwarzschild in 1916. For a black hole, the event horizon represents a one-way entrance; for a white hole, it’s exit-only.

Continue Reading

(Reblogged from trigonometry-is-my-bitch)
thesubatomic:

a Bubble freezing in extreme cold temperature.

thesubatomic:

a Bubble freezing in extreme cold temperature.

(Reblogged from trigonometry-is-my-bitch)

trigonometry-is-my-bitch:

A demonstration of the mathematical principles of the original Forth Bridge in Scotland performed at Imperial College in 1887. The central ‘weight’ is Kaichi Watanabe, one of the first Japanese engineers to study in the UK, while Sir John Fowler and Benjamin Baker provide the supports.

Photograph: Imperial College

(Reblogged from trigonometry-is-my-bitch)