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How To Learn To Use The Golden Ratio In Maths?

By Yann, published on 27/02/2019 We Love Prof > Academia > Maths > History Of The Golden Number And How To Use It

If you are a high school math student, you have heard of and studied equivalent fractions, differential equations, algebra, geometry, trigonometry (trig.), probability, Pythagorean theorem and other important mathematical concepts in the maths curriculum.

But what you may not realise is that this knowledge is built upon the maths basics that you have been taught since kindergarten and primary school. Addition and subtraction, multiplication and division are the pillars of for understanding all mathematics education and your ability to grasp and solve these math problems is what leads you now on the road to math mastery.

if you are serious about your math practice, you have studied sequences, fractions and algebraic math concepts. You will also recognise that math is not just made up of typical whole numbers but also symbols and letters which represent different parts of the number system.

Some of these special numbers are seen with pi, the distinctive Euler’s e, the special numbers i, and of course the golden ratio.

Once you have left the primary grade math classroom where the curriculum was times tables, adding and subtracting. Maths begins to open up and with so does your understanding of the world. Rounding out your knowledge in the subject is a great skill as maths is one of the common core standards for many parts of our society today.

To learn math and more about its number patterns and mathematical models lets take a look at the golden ratio.

The Parthenon is a Greek temple Plato used the golden ratio to design The Parthenon. Photo Source: Unsplash

What Is The Golden Ratio?

The golden ratio, divine proportion or golden proportion is said to be the perfect proportion that naturally occurs in nature. The term describes the relationship between two figures where the numbers of those figures are in a complementary ratio.

a+b/a = a/b = 1.618034

The ratio of the sum a + b of the two lengths to the largest (a ) is equal to that of the largest ( a ) on the smallest ( b )

For example, a rectangle which measures 12.94cm (a) by 8 cm (b) is in the golden ratio. How do we know? Let’s look at an equation.

12.94/8 = 1.6175

As you can see the mathematical model has nothing to do with a square root or area and volume. This is classed as the golden ratio simply because we are dividing the long edge (12.94) by the short edge (8) which gives us our answer and the answer matches the golden ratio sequence. It is also important to know that the golden ration can’t be made into a fraction and its decimals go on infinitely, which makes it an irrational number.

It is the irrational number All throughout the twentieth century, and even today the golden ratio continues to fascinate mathematicians, artists and architects. Photo Source: Unsplash

Mathematicians And The History Of The Golden Ratio

The golden ratio dates back to Egypt c.2600 BC, it is very old, used initially in geometry rather than arithmetic. As well as the Egyptians it may also have been used by the Pythagoreans, who may have used it to build pentagons using isosceles triangles.

  1. The first mathematical text really highlighting the golden ratio was written by Euclid c.300 BC.
  2. Plato is one of the first mathematicians to study the golden proportion exclusively as a mathematical concept. He used it to design The Parthenon
  3. Mathematician Al-Khawarizmi shines a new light on the golden ratio in the eighth century by proposing several problems of dividing a length of ten units into two parts. The solution of one of them is the initial size divided by the golden ratio.
  4. It is Fibonacci who talks about the equations along with his famous Fibonacci sequence. He found a link between the Fibonacci sequence and the golden ratio. By dividing a number in the series by the previous entry, the result comes very close to the golden ratio. This estimating becomes very accurate the further along in the sequence or, the higher in the sequence that you go.
  5. The irrationality of the golden number is taken on by Campanus through to who explores the golden ratio in geometry. He creates the golden spiral which is a logarithmic spiral. The growth factor of the spiral is equal to the golden ratio.
  6. Written about by Pacioli in his book divine proportion which was illustrated by Da Vinci.
  7. The German philosopher Adolf Zeising thinks that the golden ratio makes it possible to understand both scientific and artistic fields.

All throughout the twentieth century, and even today the golden ratio continues to fascinate mathematicians, artists and architects. It is the irrational number that gives rational meaning to beauty.

Coolmath: The Uses Of The Golden Ratio

  • Plato used it to design The Parthenon
  • The Egyptians used it to design and build the pyramids
  • Architecture: Notre Dam, the Taj Mahal and the Great Mosque of Kairouan all have golden ratio elements
  • Artists: Da Vinci, Dali and other used and continuous to use the golden ratio in the layout of their artwork.
  • Music: The ratio can be detected in the music of Bach, Debussy, Beethoven and Chopin
  • Books: the bible talks about the golden ratio number system and things being built following the ratio
  • Nature: Flowers, plants, foods and more grow in accordance with the golden ratio. Even hurricanes and its chaos follow the number lines of the golden ratios.
  • Life: Insects, animals and humans have a connection to the golden ratio. Looking at Da Vincis The Vitruvian Man drawing, you can see that the human body is created based on the golden ratio. In the modern day, psychologists have noted that attractiveness may be judged by those who have features that are in line with the golden ratio. The golden ratio is even shown in our DNA

What do you think of that for some cool math? I wonder what the statistic is that a golden ratio is just a regular number? I am guessing that the golden ratio is a true interactive math sequence that is guiding the order of operations within the divine universe.

now learn other important mathematical concepts If you are a high school math student, you have heard of and studied equivalent fractions. Photo Source: Unsplash

Why Use The Golden Ratio?

The Golden Ratio is a truly fascinating number as it finds itself everywhere, even the building blocks of our DNA follow this principle. I have no interest in the golden ratio mathematically, but it is a personal interest of mine. Don’t you find it fascinating? This exponential number has somehow permeated every corner of the universe. From galaxies to bees, from flowers to the weather.

The golden principle is interesting to me because of its logic, despite being an irrational number, it is a math fact that this sequence has a lot to offer us. You can use it when solving a math problem. You can use it to help you to design something that is aesthetically pleasing. You can even use it for some math fun and discover the golden ratio in your home or even on your own face.

You won’t find this taught in the kindergarten or a primary level classroom, but perhaps the high school math classroom was designed using the golden ratio. This is fun math that exists on the borders of math, science, philosophy, reality and discovery. This is not like linear equations, differential equations, Polynomial triangles, or the mastery of other mathematical concepts.

Indeed, high school can be fun and exciting, even with math learning. This theorem is still being discovered and explored so if you want to put your name in the history books. The golden ratio could be your opportunity to win a noble prize, get your math worksheets ready!.

As a learner of maths knowledge about the golden ratio should be added to your list of math skills. However make sure you have your foundation in arithmetic, subtracting, multiplication problems or average grade math (basic math). Because it gives you a strong foundation to understand and work from.

Ways Fun Can Help You Learn The Golden Ratio

When you are happy and having fun, you retain knowledge longer and learn easier. When you were younger math teacher may have used a math game to help you remember your times tables, calculus, adding and subtracting or for solving problems.

Learning the fun way with quizzes, puzzles, perhaps a number jigsaw. Is an interactive and engaging way to study math.

Some other ideas for learning fun:

  • Watch fun math videos
  • Attend free math peer groups
  • Go to free online math websites
  • Play online math games via apps. Sudoku is a good one
  • Ask for math help from a teacher with fun math worksheets or after school lesson plans
  • Get a math tutor who can work with the lessons plans your teachers give you.
  • Lastly, incorporate maths into things that you enjoy and your daily life.

Have fun with your mathematics, move the decimal places, create square roots, look for symmetry, twist the negative numbers, question your homework, find new solutions, solve problems and try to think outside of your grade level.

If your personal study doesn’t follow the math curriculum or core standards it’s ok. Reinforce what you need to know and play with the rest, don’t limit your mind. As the golden ratio has shown us there really is no limit.

If you have an interest in special numbers read our blog about the special number pi, the important prime number series and the rarity that is the perfect numbers.


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