Mathematical composition: How to choose between mathematics and life, such as photography and the golden section, or from life to mathematics, such as wiper and quadratic function? 600 words

Golden section and photographic composition

"Golden Section" is a geometric formula invented by the ancient Greeks, and the composition form that follows this law is considered to be "harmonious". The significance of this rule lies in providing a reasonable geometric line segment when appreciating an image work. For many painters/artists, "golden section" is a guiding principle that they must deeply understand in their current creation, and photographers are no exception.

Principle 1?

As shown in Figure A, the formula of "golden section" can be deduced from the square. Divide the bottom of the square into two halves, take the midpoint X, make a circle with the radius of line XY as the center, and the intersection point with the bottom line is Z, thus extending the square into a rectangle with a ratio of 5: 8 (Y' is the "golden section point"), a: c = b: a = 5: Fortunately, the ratio of 35MM film format is very close to this ratio of 5: 8 (24: 36).

Figure a?

Principle two?

Figure B: Through the above deduction, we get a rectangle that is considered to be perfect. Connect the upper left corner and the lower right corner of the rectangle into a diagonal line, and then make a line segment from the upper right corner to the Y' point (golden section point, see Figure A), and cross the diagonal line, thus dividing the rectangle into three different parts. Now that the golden section has been completed in theory, you can roughly arrange the scene you want to shoot according to these three areas, or flip the schematic diagram 180 degrees or rotate it 90 degrees for comparison. ?

Figure b

Trigonometry?

"Trigonometry" is actually just a simplified version of "Golden Section". Its basic purpose is to avoid symmetrical composition, which usually puts the subject in the center of the picture, which is often annoying. In figures C 1 and C2, we can see that there are four points related to the golden section, marked with a "ten" line. There are two basic ways to avoid symmetry by using the "trisection". The first one is that we can divide the picture into two areas, accounting for 1/3 and 2/3 respectively. ?

Figure C 1?

The second type: directly refer to the four "golden section" points in the figure. For example, suppose we see a very charming scenery, but we lack a subject with beautiful geometric structure, then the photo taken will only be an empty and tasteless scene. What should we do? Try to find an object that is in sharp contrast with this monotonous environment, and put this object in one of the "ten" points in Figure C2, so that the photo has an obvious anchor point and guides the audience's eyes to the whole landscape. ?

Figure C2?

Cross line?

Intersection/diagonal is actually another form of "golden section". Its basic idea is to provide a guide line to guide your line of sight, and it is ideal to connect two corners. The traditional method thinks that the top left corner is the best starting point because most people are used to browsing a picture from here. But if this diagonal line is a single straight line, it will often appear dull, so there must always be some embellishment in the picture (as shown in Figure G).

Figure g

There are two anchor points in Figure G: the boat and the gazebo. Proper ornament breaks the original symmetry.

In Figure F, a focus with multiple diagonal lines appears, which makes the audience's eyes browse in multiple directions along the guide line, making the picture lively and interesting.

Figure f

To sum up, an excellent photographic work should not only have a profound theme and content, but also have a beautiful form and harmonious composition consistent with the content. It is very helpful for beginners of photography to understand and master the golden section method in framing and use it to guide framing.