The Beauty of Story-telling in Cinema by Vika Nightingale

"After numerous requests, I finally decided to create a sequel to "First and Final Frames". Part II plays the opening and closing shots of 70 films side-by-side. Like the first video, some of the opening shots are strikingly similar to the final shots, while others are vastly different--both serving a purpose in communicating various themes. The side-by-side comparison can communicate an entire story, but also allows us to develop new theories about a given film. So once again, what can we learn from examining the first and final frames of a film? My deepest thanks to everyone for the praise and support on the first video! View Part 1 here: MUSIC: "Together We Will Live Forever" by Clint Mansell Potential SPOILERS for the following films: Sunshine Snowpiercer Biutiful 21 Grams The Prestige All is Lost Take Shelter The Impossible United 93 Vanilla Sky Ex Machina Inside Llewyn Davis Dead Man Mystery Train Melvin and Howard Fury Full Metal Jacket A Clockwork Orange Eyes Wide Shut Eraserhead The Elephant Man The Fall The Thin Red Line The New World Road to Perdition Snow Falling on Cedars The Bourne Ultimatum The Imitation Game Flight Hard Eight Inherent Vice World War Z Wild The Double The Machinist Born on the Fourth of July Brideshead Revisited Maps to the Stars The Skeleton Twins Mommy A Scanner Darkly 10 Years Milk Lost Highway Boxcar Bertha Badlands Ghost Dog: The Way of the Samurai Ratcatcher Ida Raise the Red Lantern Gattaca Kundun Bringing Out the Dead A Most Wanted Man The Curious Case of Benjamin Button The Social Network Jack Goes Boating Submarine Half Nelson Eternal Sunshine of the Spotless Mind Babel Django Unchained True Grit Vertigo Oldboy Apocalypto Dawn of the Planet of the Apes Gladiator Mad Max: Fury Road World's Greatest Dad Copyright Disclaimer: Under Section 107 of the Copyright Act 1976, allowance is made for "fair use" for purposes such as criticism, comment, news reporting, teaching, scholarship, and research. Fair use is a use permitted by copyright statute that might otherwise be infringing. Non-profit, educational or personal use tips the balance in favor of fair use."

Magic Squares by Vika Nightingale

An arrangement of distinct numbers in a grid, where the numbers in each row, column and main diagonals add up to the same sum, is a peculiar example of ancient mathematics. 

2 7 6
9 5 1
4 3 8

(Here the sum is 15.)

The constant that is the sum of every row, column and diagonal is called the magic constant, M. Every normal magic square has a constant dependent on n, calculated by the formula: 

M = [n(n2 + 1)] / 2. 

For normal magic squares of order n = 3, 4, 5, 6, 7, and 8, the magic constants are, respectively: 15, 34, 65, 111, 175, and 260.

The earliest example is the one of the Lo Shu square (as early as 650 BC) in China. In Albrecht Dürer's magic square the sum 34 can be found in the rows, columns, diagonals, each of the quadrants, the center four squares, and the corner squares. 

16  3   2  13
5  10  11  8
9   6   7  12
4  15  14  1

A magic square is also featured on the walls of Sagrada Familia in Barcelona, designed by Gaudi. 

In the mid-nineteenth century, an amateur puzzle enthusiast in New York named Palmer Chapman made a physical model of a fourth-order magic square but left out one piece so that the individual cells could slide around. This was known as the 15 Puzzle. In the 1970’s, Erno Rubrik, a Hungarian designer, was attempting to recreate the 15 puzzle in three dimensions when he came up with the Rubik’s Cube.