the first version is the easier but also boring for the eye, the sequence rectangular-square-square and repetitive, try to use diagonal cut, open space and vertical cut to help the movement of the story and action.
Constructing Reality Pt.3 - Fibonacci and the Golden Spiral
If we want to understand the mystery behind reality, we have to take a look at its patterns. The language of nature gives us a rash of information on how the whole universe moves and grows. The same pattern can be noticed in blooming plants, evolving populations, crowd behavior, artistic and architectural expressions, and even in the movement of whole galaxies. Referring to the pattern that is all around us, Leonardo da Vinci spoke: “Learn how to see. Realize that everything connects to everything else.”
The human mind has a natural sense for artistic harmony, always feeling drawn to a very special kind of proportion. If we have to choose the most harmonic of the rectangles below, we intuitively choose the one based on the golden ratio Phi Φ, a mathematic term for two quantities, of which the ratio of the small part (a) to the large part (b) is the same ratio as the large part (b) to the whole (a+b). However, Phi is an infinite number, beginning with 1,618033…, which means that all visual images can only approach the golden ratio, but never fully reach it.
The golden ratio rectangle is the visual version of a specific numeric pattern. This pattern has been known for thousands of years, first mentioned as mātrāmeru in the Sanskrit treatise Chandahshastra by the indian mathematician Pingala around 400 b.c. Even though it has also been known in ancient Greece, the pattern is named after the italien mathematician Leonardo da Pisa, better known as Fibonacci. The Fibonacci sequence describes an infinite series of numbers, in which the sum of two consecutive numbers results in the proximately next number. Demonstrated and easier understood: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144… The connection between the golden ratio and the Fibonacci sequence becomes clear when we continue to construct the golden ratio rectangle, or the Fibonacci squares, into a possible infinity. But again, since Phi is an infinite number, the Fibonacci numbers can only approach but never reach it.
While the Fibonacci sequence and the Fibonacci squares seem to be abstract geometry, the next step will make us comprehend the link to nature and mother earth. The so called Golden Spiral, also known as the Fibonacci Spiral, is the consequent result of the previously created basic pattern. The Golden Spiral is the model for a huge amount of natural designs and developments that exist in our dimension. While the typical Fibonacci Spiral expands its widths in 90 degree sections, another spiral we often find in nature expands its widths in 180 degree sections. Both spirals are golden.
We can see Fibonacci in many plants on our Earth. By following the Golden Spiral, leaves are provided an optimal light saturation and blossoms a promising seed dispersal, as imposingly seen in the Sun Flower. The same double spiral can be seen in the petals of the lotus flower, which is the best example of the nearly perfect Fibonacci creation. We also see the golden 180°spiral in animals, for example in snail and nautilus shells or in the curling of animal tails. Fibonacci does not only appear as the spiral in animals, but also in connection to reproductive dynamics, for example in bees and rabbits, where every generation increases its population by 1,6. When it comes to humans, our whole body shows golden proportions, from our face, to our limbs and hands and even where we probably don’t expect it – our DNA molecules. DNA molecules spin according to the rules of the Golden Spiral, for a cycle of the double helix measures exactly 34 angstroms in length and 21 angstroms in width. Fibonacci is not only around us, but also inside of us.
Truth is that no visual construct that can be perceived with our senses could fully reach the exact golden ratio proportion, because we create our reality based on boundaries and not on infinite ideas. Yet, the approach to rediscover our own perfect harmony is a part of all of us, when we strive for enlightenment and peace.
The square root of 2 equals 1.41421356237… Multiply this successively by 1, by 2, by 3, by 4 and so on, and write down the integer part of each result. Beneath this sequence, make a second list of the numbers missing from the first sequence.
Then the differences between the upper and lower numbers in these pairs are 2, 4, 6, 8, 10, 12, 14, 16, 18…
- the letter j
- the letter m
- the name jo
- the name mike
- this includes square numbers and square roots
- also rectangles
- circles within circles
- shower heads
- shower heads and angles combined
- jets in shower heads
- tribonacci sequences
- especially square staircases
- staircases made of squares
- staircases with numbers
- the number 2017
- also 20 and 17
- the number 3
- actually all numbers from 0-24
- also hopscotch
- especially hopscotch labelled from 0-24
- THE ENTIRETY OF JUNIOR STUDENT PROBLEMS
@hyunguponew asked: *whispers into the void* Ravi nightmare expansion
A/N: Ok my friend, I did the best I could with the specter of your immense talent looming over my shoulder. Stop cringing, it’s true. I hope you like it and if you don’t, lie. :P
This is a drabble expansion of a reaction I wrote here.
Your cry of distress echoed in his ears even though you weren’t actually there to make a sound. Choking on his own ragged breaths Ravi sat up in tangled sheets. It had felt so real. Closing his eyes he could still see you thrashing in the water, calling out to him to save you. But he couldn’t move. Unable to do anything but watch, tears streaming down his face as you drowned. He ran a hand through sweat-slick hair. His throat felt sore and he remembered screaming your name at the top of his lungs. Shit. He hoped he hadn’t been too loud. Wouldn’t look good to wake the whole hotel.
Swiping his phone off the night stand beside him he fumbled to unlock it. It took a few tries. Ravi’s hands were shaking and he couldn’t get the right sequence. The square inch of his brain that was still rational knew you were home asleep but he couldn’t stop hearing your screams. He never, ever wanted to hear that in real life.
Finally gaining access the screen seemed extra bright as he pressed one to speed dial you. The fear scratched incessantly down his spine that maybe you had been hurt and somehow called out to him. Stranger things had happened he supposed. They show that kind of stuff on TV all the time. The point was, he was here, you were there and if something had happened to you he didn’t know what he’d do.
Why weren’t you answering the damn phone? Ravi knew you kept it near when he was away. Maybe you couldn’t. Maybe you were dyi–
Your sleepy voice punched through his chest and he felt like he could breathe for the first time in minutes. “Babe? Baby are you ok?”
Something in his voice must have alarmed you because you sounded more alert. “Yeah, Rav. I’m fine. What’s going on?”
Tension fled his muscles as he tilted back onto the bed. His throat knotted and he knew if he tried to talk he’d lose it. Draping an arm over burning eyes he lay there trying to get himself under control.
“Ravi? Wonsik, what’s wrong? You’re scaring me.”
It hadn’t been his intention to scare you. Clearing his throat he fought to keep his voice steady. “I’m fine, I promise. I just missed you.”
There was a moment of suspicious silence from the other end of the line. “That’s it? You’re calling in the middle of the night because you missed me? Nothing happened?” Your voice didn’t sound upset, just worried and he felt even worse for overreacting. But there was no help for it. What was done was done and he knew he couldn’t have made it through the rest of the night without knowing you were ok.
“I’m sorry I worried you. I just…needed to hear your voice.” Silence fell between you. The screams came back in his head and he shuddered. “Can you do something for me, please?”
“Can you,” he took a steadying breath, fingers tracing the edge of the sheet laying on his chest. “Can you just talk to me for a while?”
With his eyes closed he could almost pretend the slight chuckle he heard came from the same room. “Well that’s random. What do you want me to talk about?”
“Anything. Everything. I don’t care.”
He heard rustling as you presumably made yourself comfortable. You told him about your day. About the new restaurant you tried and how you thought he’d love it. The gifts for his sister’s birthday that were supposed to be from both of you that you’d picked out on your own. You always seemed to be pulling his ass out of the fire one way or the other.
As he listened a lassitude came over his body. He should warn you that he was about to fall asleep but he didn’t want to hang up. Ravi wasn’t ready to let you go in more ways than one. The last thing he heard was the soothing sound of your voice as he drifted off.
Today marks the 77th birthday of one of the world’s most eminent mathematicians: John Horton Conway, currently Professor of Mathematics and John Von Neumann Professor in Applied and Computational Mathematics at Princeton University. Conway earns my admiration for countless cool contributions in many branches of mathematics.
Conway became interested in mathematics at a very early age: as a four year old kid, he could already recite the powers of two, and at the age of eleven his ambition was to become a mathematician.
A selection of the topics Conway has touched:
Conway invented a number system called the surreal numbers, which form the largest possible ordered field (in some sense). Study of this system was motivated by mathematical games, which could be solved using the surreal numbers. Conway wrote the delightful book On Numbers and Games about it.
One of the early and still celebrated examples of a cellular automaton, the Game of Life, is a creation of Conway, whose early experiments were done with pen and paper, long before personal computers existed.
Conway’s 15 theorem states that if a positive definite quadratic form with integer matrix represents all positive integers up to 15, then it represents all positive integers.
Together with Michael Guy he established the classification of convex uniform polychora (4-dimensional analogues of polyhedra), discovering the grand antiprism in the process.
Conway extensively investigated lattices in higher dimensions, and determined the symmetry group of the Leech lattice.
In knot theory, there is a variant of the classical Alexander polynomial named the Alexander–Conway polynomial which is an invariant for knots. He also developed the beautiful tangle theory, which built a bridge between knot-like structures and fraction arithmetic.
Conway played a major role in the classification of finite simple groups. He discovered the three sporadic Conway groups, based on the symmetry of the Leech lattice, and was the primary author of the ATLAS of Finite Groups.
He extended the Mathieu group to the Mathieu groupoid and presented it as a sliding tile puzzle played on a projective plane.
Conway proposed the Turing-complete esoteric programming language FRACTRAN, in which a program is an ordered list of positive fractions together with an initial integer input value.
Ever heard of Conway’s icosian numbers? They’re a specific set of quaternions and exhibit lots of symmetry.
Conway’s doomsday algorithm can be used to calculate days of the week. The story goes Conway’s computer isn’t protected by passwords, but by a quiz of random dates, in order to improve his mental arithmetic speed.
Together with Simon Kochen he proved the free will theorem. In Conway’s own wording, the theorem states that “if experimenters have free will, then so do elementary particles”.
The LUX method is an algorithm to generating magic squares.
Conway introduced and analyzed the look-and-say sequence and proved the Cosmological Theorem: every sequence eventually splits into a sequence of “atomic elements”, finite subsequences that never again interact with their neighbors.
As a spectacular counterexample to the converse of the intermediate value theorem, Conway defined the monstrous discontinuous base 13 function, which takes on every real value in each interval on the real line.
Conway’s criterion gives a simple but powerful sufficient criterion for a prototile to tile the plane.
Pinwheel tilings are the first known non-periodic tilings to each have the property that their tiles appear in infinitely many orientations, and were based on a construction due to Conway.
ok so i am very excited to have finally gotten 100% on every floor of every labyrinth and i know how annoying and confusing map-making can be so i am now sharing them with all of u wonderful people if you need them so HERE YA GO (jesus this is gonna be a long post buckle up)
Yuna’s first sending in FFX. That scene is, in my opinion, the most visually stunning, beautifully scored, and heartbreaking scene Square’s ever made. When you realize the woman crying right when Yuna starts dancing
And then fully starts breaking down near the end of the sending
Is the mom who was playing with her three kids before Sin attacked Kilika
Like I don’t think any FMV sequence Square Enix’s CGI team’s made since has packed that much of an emotional punch