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Alternate Versions. Rate This. Director: Fatih Akin. Hammer was hoping to extend their life by coming up with some new series and their collaboration with Shaw Brothers productions was perhaps both ahead of its times while a year or three too late to save the company.
It was a glorious failure that deserves to be seen again now that present day technology can give viewers a better estimation of the movie's intended form.
It is surprisingly entertaining and compulsively watchable. It's still somewhat confusing if you are looking for a discreet, beginning-middle- end story progression.
Just by turning his head slightly to the side and raising an eyebrow Peter Cushing is a treat, nobody can look concerned or impart a sense of dire urgency into an audience like Peter Cushing: It may be an odd movie but it does feature some of his best work at appearing concerned and some of the urgencies that he imparts within viewers are the most dire of his career.
Yeah, he was getting old and tired and probably looked upon the movie as an expense paid trip to China to help him forget the sorrow of his wife's passing.
But by golly he made the movie and if he means anything to you it simply must be seen because it is his last screen turn as one of his classic Gothic horror characters.
Try it again, make sure it's a widescreen version, pop plenty of popcorn, perhaps an adult beverage or two, and put down the lights.
Turns out it's not a bad movie after all. Prime Video has you covered this holiday season with movies for the family. Here are some of our picks to get you in the spirit.
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Official Sites. Company Credits. Technical Specs. Plot Summary. Plot Keywords. Parents Guide. External Sites. Leonardo da Vinci 's illustrations of polyhedra in Divina proportione  have led some to speculate that he incorporated the golden ratio in his paintings.
But the suggestion that his Mona Lisa , for example, employs golden ratio proportions, is not supported by Leonardo's own writings.
The dimensions of the canvas are a golden rectangle. A huge dodecahedron, in perspective so that edges appear in golden ratio to one another, is suspended above and behind Jesus and dominates the composition.
A statistical study on works of art of different great painters, performed in , found that these artists had not used the golden ratio in the size of their canvases.
The study concluded that the average ratio of the two sides of the paintings studied is 1. Many books produced between and show these proportions exactly, to within half a millimeter.
According to some sources, the golden ratio is used in everyday design, for example in the proportions of playing cards, postcards, posters, light switch plates, and widescreen televisions.
The golden ratio is also apparent in the organization of the sections in the music of Debussy 's Reflets dans l'eau Reflections in Water , from Images 1st series, , in which "the sequence of keys is marked out by the intervals 34, 21, 13 and 8, and the main climax sits at the phi position".
The musicologist Roy Howat has observed that the formal boundaries of Debussy's La Mer correspond exactly to the golden section. Pearl Drums positions the air vents on its Masters Premium models based on the golden ratio.
The company claims that this arrangement improves bass response and has applied for a patent on this innovation. Though Heinz Bohlen proposed the non-octave-repeating cents scale based on combination tones , the tuning features relations based on the golden ratio.
As a musical interval the ratio 1. Johannes Kepler wrote that "the image of man and woman stems from the divine proportion.
In my opinion, the propagation of plants and the progenitive acts of animals are in the same ratio". The psychologist Adolf Zeising noted that the golden ratio appeared in phyllotaxis and argued from these patterns in nature that the golden ratio was a universal law.
In , the journal Science reported that the golden ratio is present at the atomic scale in the magnetic resonance of spins in cobalt niobate crystals.
However, some have argued that many apparent manifestations of the golden ratio in nature, especially in regard to animal dimensions, are fictitious.
The golden ratio is key to the golden-section search. The golden ratio is an irrational number. Below are two short proofs of irrationality:.
If we call the whole n and the longer part m , then the second statement above becomes. Another short proof—perhaps more commonly known—of the irrationality of the golden ratio makes use of the closure of rational numbers under addition and multiplication.
The golden ratio is also an algebraic number and even an algebraic integer. It has minimal polynomial. Having degree 2, this polynomial actually has two roots, the other being the golden ratio conjugate.
The vertices of a regular icosahedron are those of three mutually orthogonal golden rectangles. There is no known general algorithm to arrange a given number of nodes evenly on a sphere, for any of several definitions of even distribution see, for example, Thomson problem.
However, a useful approximation results from dividing the sphere into parallel bands of equal surface area and placing one node in each band at longitudes spaced by a golden section of the circle, i.
This method was used to arrange the mirrors of the student-participatory satellite Starshine Application examples you can see in the articles Pentagon with a given side length , Decagon with given circumcircle and Decagon with a given side length.
Both of the above displayed different algorithms produce geometric constructions that determine two aligned line segments where the ratio of the longer one to the shorter one is the golden ratio.
The golden triangle can be characterized as an isosceles triangle ABC with the property that bisecting the angle C produces a new triangle CXB which is a similar triangle to the original.
In a regular pentagon the ratio of a diagonal to a side is the golden ratio, while intersecting diagonals section each other in the golden ratio.
This result is a straightforward consequence of the intersecting chords theorem and can be used to construct a regular pentagon, a construction that attracted the attention of the noted Canadian geometer H.
Coxeter who published it in Odom's name as a diagram in the American Mathematical Monthly accompanied by the single word "Behold! The golden ratio plays an important role in the geometry of pentagrams.
Each intersection of edges sections other edges in the golden ratio. The pentagram includes ten isosceles triangles : five acute and five obtuse isosceles triangles.
The acute triangles are golden triangles. The obtuse isosceles triangles are golden gnomons. The golden ratio properties of a regular pentagon can be confirmed by applying Ptolemy's theorem to the quadrilateral formed by removing one of its vertices.
Consider a triangle with sides of lengths a , b , and c in decreasing order. A golden rhombus is a rhombus whose diagonals are in the golden ratio.
The rhombic triacontahedron is a convex polytope that has a very special property: all of its faces are golden rhombi.
The mathematics of the golden ratio and of the Fibonacci sequence are intimately interconnected. The Fibonacci sequence is:.
A closed-form expression for the Fibonacci sequence involves the golden ratio:. The golden ratio is the limit of the ratios of successive terms of the Fibonacci sequence or any Fibonacci-like sequence , as shown by Kepler : .
For example:. The golden ratio has the simplest expression and slowest convergence as a continued fraction expansion of any irrational number see Alternate forms above.
It is, for that reason, one of the worst cases of Lagrange's approximation theorem and it is an extremal case of the Hurwitz inequality for Diophantine approximations.
This may be why angles close to the golden ratio often show up in phyllotaxis the growth of plants. The multiple and the constant are always adjacent Fibonacci numbers.
The golden ratio appears in the theory of modular functions as well. This gives an iteration that converges to the golden ratio itself,. These iterations all converge quadratically ; that is, each step roughly doubles the number of correct digits.
The golden ratio is therefore relatively easy to compute with arbitrary precision. The time needed to compute n digits of the golden ratio is proportional to the time needed to divide two n -digit numbers.
An easily programmed alternative using only integer arithmetic is to calculate two large consecutive Fibonacci numbers and divide them.
The ratio of Fibonacci numbers F and F , each over digits, yields over 10, significant digits of the golden ratio. Both Egyptian pyramids and the regular square pyramids that resemble them can be analyzed with respect to the golden ratio and other ratios.
The isosceles triangle that is the face of such a pyramid can be constructed from the two halves of a diagonally split golden rectangle of size semi-base by apothem , joining the medium-length edges to make the apothem.
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