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News from Mathnasium of Oak Creek

Geometry, The Golden Ratio, & Memorable Logos

Apr 20, 2022

Do you ever wonder how the logos of popular companies like Apple, Nike, Toyota, Nasa, and others are designed? If you look at a logo, you may not view it as an artistic masterpiece, but it is a mathematical masterpiece. Math plays an important part in creating logos, the symmetry of logos all follows strict mathematical formulas. 

 

Geometry is fundamental to graphic design, making simple yet compelling designs. . Several factors contribute to this: a logo that utilizes math in its design is aesthetically simple yet pleasing, has a quick impact, and is versatile, which is what designers and businesses need to make their business stand out.

Here are examples of a few famous logos and the math that went into their creation.

 

Apple:

The Apple logo may look very simplistic at a first glance, but if you tried to replicate it, the robust mathematical formulas that go into it may stop you. The Apple logo utilizes a replication of the Fibonacci sequence that is not obvious to the eye. Specifically, seven circles of different sizes are created that will be placed in specific positions. All this makes it so that the bite, curves of the top, and the blade are the same size. That is why creating the perfect Apple logo is not a very easy task.

 

British Petroleum (BP):

Numerous concentric circles form British Petroleum’s simple green and yellow sunflower logo. Much like the circles used in the Apple Inc. logos, the Fibonacci Sequence determined their dimensions.

Twitter:

Twitter's logo is based heavily on perfect circles. Three sets of three interlocking circles were used to create the new, streamlined Twitter bird. Another example of a logo created using math.

 

Toyota:

The logo of Toyota consists of three ovals, overlapping ellipses. Toyota states that the ovals in their logo symbolize the unification of the hearts of its products and consumers, a symbol very unique to the company. The logo is yet another example of impactful graphic design that uses math.

 

If you measure the distance between the bottom inner edge of the small horizontal oval, the bottom of the outer edge of the large horizontal oval, and the distance between the extreme top and bottom edges of the large oval, you’ll find they are in a Golden Ratio proportion.

Batman:

The famous Batman logo has a complex shape created using parabolas and linear equations. The math behind it is coordinate geometry

 

Pepsi:

The underlying backbone of the Pepsi logo follows the golden ratio. This simple and effective logo is created by intersecting circles with a set proportion to each other.

Golden Ratio creates a balance that is pleasing to the eye. It’s represented by the Greek letter Phi (Φ), and it is expressed as 1:1.618033987. Several intersecting circles of various sizes form the red, white, and blue Pepsi logo. The ratio is formed by dividing a line into two unequal lengths. The sizes of those circles are in a Golden Ratio proportion to one another.

 

 

National Geographic:

Remember the yellow square in the National Geographic logo? Have you ever wondered why that simple logo appears to be so appealing? The answer is the Golden Ratio. The yellow rectangle of the National Geographic logo is a simple Golden Rectangle. The ratio of the outer width to the external length, and the inner width to the inner length, is 1:1.618.

 

 

Most people don’t think about the geometrical knowledge that goes into designing and creating art. With a trained eye and prior knowledge, you can begin to identify the blueprints of a successful logo design!