you've probably heard of The Golden Rule and you might even be using it in your daily life but there is another little bit of gold that is playing a role in your daily life that you might not know about the Golden Ratio or 1.618 the golden ratio is a proportion based on the Fibonacci sequence and can be found almost anywhere in life probably even in the room where you are sitting for those who do not know the Fibonacci sequence is a series of numbers where each number is the sum of the two previous numbers for example 1 1 2 3 5 8 is a basic example of the Fibonacci sequence the sums are all called Fibonacci numbers these special little numbers can be found in architecture art music and even in nature here we will explore some of the many places where you can find the golden ratio and the Fibonacci sequence amazing number 10 the Great Pyramids of Giza the ancient Egyptians have intrigued the human race for thousands of years possibly the most famous point of interest in Egyptian culture or the Great Pyramids of Giza the most popular question about the pyramids is how they were built but maybe the question should be why they were built specifically why they were built in such a specific orientation when aerial photographs first became available of the Great Pyramids it became apparent that there is a pattern to their placement the first place that the ratio is seen is in the geometry of the the pyramids when applying the Pythagorean theorem to the height of the base of one of the internal triangles you will notice that the hypotenuse is just .25% off of a perfect golden ratio triangle otherwise known as a Kepler triangle well this could be a happy accident we are guessing that these ancient mathematicians were attempting to be as exact as possible when dragging these 8 ton blocks across the desert the next place you can find the golden ratio in the pyramids is their placement next to to each other most of the pyramids have been placed in the exact orientation of a five Matrix grid which is based on the golden ratio this can be seen in the pyramids of queens and the pyramids of kufu and cafrey while the golden ratio can be found in many more places in the complex of the pyramids maybe the most astounding can only be seen from above when drawing lines through the base corners of the pyramids you will notice that they begin to intersect at a specific point mathematicians then begin to notice a familiar shape for form when looking at the illustration from above the spiral shape that is seen in so many golden ratio related figures is seen once again in the placement and orientation of the Great Pyramids of Giza just to clarify a golden spiral is a spiral that grows by a factor of five as it increases in size these spirals can also be fit into the five Matrix number nine the Taj Mahal one more wonder of the world that successfully implemented the golden ratio into its architecture the Taj Mahal it's no big secret that the Indian people have made a great contribution to the field of mathematics so it should come as no surprise that their most famous building is Rich with mathematical references the first and most obvious place you see the golden ratio on the Taj Mahal is on its rectangular base where the FI Matrix can be seen in addition to this you can see other buildings on the Taj Mahal premises that also implement the FI Matrix into its architecture number eight the Mona Lisa one of the most famous pieces of Art in human history is also one of the most famous examples of the use of the golden ratio the Mona Lisa Leonardo da Vinci was a polymath who held talents in subjects from architecture to astronomy what is best known for his contributions to Art in many of his Works he was able to combine his talents and Mathematics with his artistic ability and the Mona Lisa was no exception throughout the picture you can draw the golden rectangle for example the space between her eyes can be divided into golden rectangle meaning that a golden rectangle exists around her head furthermore her entire body can be fit into a golden rectangle you can even draw a golden spiral from the center of her nose over her head and through her shoulders many of Da Vinci's Works where the golden ratio can be found is within the famous Vitruvian man as well as the Last Supper nowadays artists look to incorporate the golden ratio within their Works in an attempt to emulate the masterpieces of Renaissance number seven spiral galaxies the examples of the Fibonacci sequence and the golden ratio that we have provided so far may lead you to think that this is some man-made and contrived conspiracy theory put forth by mathematicians around the world but when we look to Nature we can see that this is no accident it almost seems Divine one of the most astounding places that we find the golden ratio in nature is at its most grand scale the cosmos the golden spiral can be seen across the Universe in the shape of spiral galaxies and even in our Milky Way galaxy if you look at our galaxy you can calculate the familiar logarithmic growth by a factor of five as the Galaxy expands but the galactic implementation of the golden ratio doesn't end here the shape of the Earth and Moon are also related to the golden ratio when placed next to each other the radius of the Moon plus the radius of the Earth equal the square root of five in addition to this the triangle that can be drawn using the radius of the Earth as the base will create a triangle with the hypotenuse measuring fi another example of this golden spiral that can only be seen from space is the shape of hurricanes look at any satellite picture of a hurricane and you can once again see the spiral Forum in the Raging Winds of Nature's Most destructive force number six flower petals one of the most famous examples were the Fibonacci series and the golden ratio are seen in nature is within plants the Fibonacci series can often be found in in the number of seeds or petals in many flowers and the golden spiral can be found within the shape of the entire flower many flower petals come in quantities that are Fibonacci numbers for example lilies and irises have three petals buttercups have five petals and daisies can be found with 34 55 and 89 petals if you look at pine cones and pineapples from the bottom you will notice that spines of these two plants are oriented in clockwise and counterclockwise wise spirals the number of lines that make these spirals are both Fibonacci numbers flowers like roses have petal Arrangements that are golden ratios next time you're out in the garden see how many of your own plants follow these Fibonacci Trends number five DNA the golden ratio is so abundant it even exists within your DNA you can find the golden ratio in the Fibonacci sequence in numerous places throughout the deoxy ribonucleic acid that makes up the human body maybe the most obvious example is the actual size of human DNA which measures 34 angstrum units long by 21 angstrom units wide both of these are Fibonacci numbers it is even reported that a cross-sectional view of a DNA molecule shows a decagonal shape a decagon can be created by rotating a pentagon by 36° using the diagonals of the pentagons that can be found in the fractals of a DNA cross-section you can see the golden ratio within the portions of the diagonals and the sides which would be five too number four music as we've said before the golden ratio exists across all subjects including music in some of the world's most popular pieces of music the golden ratio is seen in timing and pacing it is speculated that such pieces that Implement a golden ratio based pattern are more pleasing to the ear in most of these examples mathematicians have broken songs down by the golden mean 618 one of the most famous examples of this is Beethoven's Fifth Symphony where the golden ratio is used in multiple sections throughout the song mosart has also been reported using the golden ratio in many of his sonatas nowadays you can find many composers musicians artists trying to implement the golden ratio into their songs number three human facial construction you've probably heard people saying that humans are naturally attracted to facial symmetry that symmetry is created by the Golden Ratio people often say the Mona Lisa is one of the most pleasing paintings to look at and it's no coincidence that the golden spiral that shapes her face is similar that of most humans many of the people that Society deems most attractive are the ones whose face most closely fits into the five Matrix that a person's face fits into plastic surgeons even use programs that help to digitally alter someone's face so it better fits the golden ratio this allows them to show their patients how their face can be surgically altered to look more attractive facial recognition software is also based on the golden ratio number two advertising companies are always looking for the best ways to advertise to their potential customers and the use of the golden ratio is one of the most effective techniques we already know that faces that loosely associated to the Golden Ratio or found most appealing and you will find that these are the type of people that are being sold you can also find the golden ratio in the logos of some of the world's most popular brands such as Toyota or Pepsi the golden ratio is a powerful tool for website and graphic designers many of your favorite sites will be based around the golden Matrix or the golden rectangle take a look at the most basic templates on some free web Builders and you will notice that most of them share a very similar look to Golden Ratio grids number one anatomy of living things earlier we mentioned one of Leonardo da Vinci's most famous works the Vitruvian Man one of the reasons that it was such a famous drawing is because it outlined the immense proportionality of the human body for example you can see the golden ratio in the length of the human head the breadth of the shoulders the distance from the top of the head to the fingertips and even the length of your forearm the consistency of the number five in the human body is also related to the golden ratio we have five appendages on our torso two arms two legs one head on each of our arms and legs we have five appendages in fingers and toes on our head we have five protruding appendages in two ears two eyes and a nose finally as we all know we have five senses other groups in the animal kingdom also have body proportions based on the Golden Rule the most visually obvious example are insects and their segmented bodies from the galaxies above us right down to our DNA you can find the golden ratio in almost every aspect there are plenty of other examples out there of how the golden ratio plays a role in your day-to-day activities but we just listed some of our favorites let us know some of your favorite ways the golden ratio affects your life in the comments below thanks for 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