Golden Ratio Design Made of Quotations about Math and Nature

Golden Ratio design on a mens crew neck t-shirt in black. The design is made from tiny, positive quotations about the connection between Phi and the universe!

Golden Ratio design on a mens crew neck t-shirt in black. The design is made from tiny, positive quotations about the connection between Phi and the universe!

Our Golden Ratio design is made from quotations about the connection between math & nature and in the shape of a Golden Spiral and Golden Rectangle. The Golden Ratio, a.k.a Phi (represented by the Greek symbol Φ), a.k.a the Golden Mean, a.k.a the Golden Section, is woven throughout so many aspects of our human existence and the universe we live in. And yet we are mostly oblivious to its power over our subconscious. This power attracts us like moths to a light except in this analogy the light is art, beauty, and our natural sense of ‘proper’ proportions. Nature is equally beholden to the influence of the Golden Ratio.

“Phi can be found throughout the universe; from the spirals of galaxies to the spiral of a Nautilus seashell; from the harmony of music to the beauty in art.”~Bruce Rawles

Golden Ratio = Φ

Here is a good summary of Phi: “A straight line is said to have been cut in extreme and mean ratio [The Golden Ratio] when, as the whole line is to the greater segment, so is the greater to the less.” ~Euclid (323 BC to 285 BC). Symbolically this can be represented by: A + B is to A as A is to B = Φ ≈ 1.61803
Our Golden Spiral design shows this relationship as both the Golden Spiral and a series of Golden Rectangles arranged in Fibonacci Tiling.

The Golden Rectangle

The largest rectangle and the largest square are in proportion to each other such that the length of one side of the square ≈ 1.61803 of the long side of the rectangle. The series of Golden Rectangles rotate 90 degrees and shrink proportionate to Phi. It is called Fibonacci Tiling because the ratio of volumes of the squares within each rectangle follow the Fibonacci series (take one number (starting and add the previous to get the next — 1, 1, 2, 3, 5, 8…).

Draw your own Golden Rectangle by following along with this animated gif. Start with a square and use a string or ruler to handle the angled line that swings down.

The Golden Spiral

Like Fibonacci Tiling, the Golden Spiral within the design uses the Golden Ratio in that the growth factor of each quarter turn is Phi (approximately 1.61803). You can find countless examples in nature making use of this growth rate. Look directly over a pinecone or a succulent plant and you will see this pattern at use by nature! Look at satellite imagery of a hurricane or telescope imagery of a spiral galaxy and you will see this pattern at use by the universe! Look at the proportions of a human face or the shape of a human ear! You will see this pattern!

If you want to draw your own Golden Spiral you can do so by first drawing the Golden Rectangle series as Fibonacci tiling. Then, using each resulting square, draw a quarter circle connecting two diagonals in the square and rotate 90 degrees doing the same to the next square.

The Golden Ratio in Art Composition, Design, and Architecture

It cannot be overstated how important the Golden Ratio is in the things humans tend to find visually appealing. Why that is may very well be connected to why this ratio shows up in nature. Perhaps we are attuned to it for some reason. It’s fun to imagine what that reason may be. Do a quick Google image search for the connection between the Golden Ratio and Art, Design, Architecture to see just how ubiquitous this ratio is.

“In order to understand the universe you must know the language in which it is written and that language is mathematics.” ~Galileo Galilei

The Fibonacci Sequence and the Golden Ratio

If you take two sequential Fibonacci numbers and divide larger one by the smaller one you will approach Phi. The resulting number will get closer and closer to Phi the deeper into the Fibonacci series you go!

Take a look at this table showing the first 20 digits of the Fibonacci series. By taking any number in the series and dividing it by the previous number in the series we get the resulting ratio in the 2nd column. The third column shows the difference between this resulting ratio and the Golden Ratio. The last three columns just continue the series for the 11th through 20th numbers in the Fibonacci series. As you can see the further in to the Fibonacci series we go the closer these ratios approach Phi.

A table exploring the relationship between the Golden Ratio and the Fibonacci series.

A table exploring the relationship between the Golden Ratio and the Fibonacci series.

A close up look at our Golden Ratio design on a mens crew neck t-shirt in black. The design is made from tiny, positive quotations about the connection between Phi and the universe!

A close up look at our Golden Ratio design on a mens crew neck t-shirt in black. The design is made from tiny, positive quotations about the connection between Phi and the universe!

Quotations used in this design

Here are all of the quotations in Think Positive Apparel’s Golden Ratio design:

“Everything in the universe that wants to be successful has to base its existence on the golden ratio.” ~Oliver Grant

“The Fibonacci Sequence turns out to be the key to understanding how nature designs… and is… a part of the same ubiquitous music of the spheres that builds harmony into atoms, molecules, crystals, shells, suns and galaxies and makes the Universe sing.” ~ Guy Murchie ∞

“Without mathematics there is no art”~Luca Pacioli

“A straight line is said to have been cut in extreme and mean ratio [The Golden Ratio] when, as the whole line is to the greater segment, so is the greater to the less.” ~Euclid

“In order to understand the universe you must know the language in which it is written and that language is mathematics.” ~Galileo Galilei

“Phi can be found throughout the universe; from the spirals of galaxies to the spiral of a Nautilus seashell; from the harmony of music to the beauty in art.”~Bruce Rawles

“The description of this proportion as Golden or Divine is fitting perhaps because it is seen by many to open the door to a deeper understanding of beauty and spirituality in life.” ~HE Huntley

“The Golden Ratio has inspired thinkers of all discipline like no other number in the history of mathematics” ~Mario Livio

a + b is to a as a is to b = Φ
1.61803…

The Golden Ratio Design is made from the Golden Spiral and a series of Golden Rectangles. These shapes are made from tiny words. The words are quotations about the connection between the Golden Ratio and the universe.

The Golden Ratio Design is made from the Golden Spiral and a series of Golden Rectangles. These shapes are made from tiny words. The words are quotations about the connection between the Golden Ratio and the universe.

What do you think of the Golden Ratio

Join the conversation and let us know your thoughts on the Golden Ratio, Golden Rectangle, Golden Spiral, or its connection to nature!

Elephant Symbolism and the Warrior III Yoga Pose

Look closer! Elephant symbolism affirmations create this design of an elephant doing a Warrior III yoga pose!

Charge through obstacles today when you apply whichever words jump out at you first. Each time you look into this Elephant Warrior III design you will see different ones. You have been them all before and can be them all again! See how the attitudes you read first fit in your day today.

An Elephant doing Yoga

“Remember, it doesn’t matter how deep into a posture you go – what does matter is who you are when you get there.” ~ Max Strom

Elephants aren’t exactly known for their physical flexibility which is the number one excuse people use to avoid starting a yoga practice. The amazing thing about yoga is that it doesn’t matter how flexible you are! Whether you are an advanced yogi touching your head to your knee with straight legs or a brand new yogi bending your legs a ton to get that forehead to touch, anyone doing their best on the mat benefits just as much!

So, how does an elephant do Warrior III pose (aka Virabhadrasana III)? Practice! Perseverance and practice! Perseverance, patience, and practice. While using these three ingredients, anyone can do any yoga pose. And at every stage of the posture we gain just as many benefits as the people adding more layers to their own practice.

Elephant Symbolism

Here are some of the elephant symbolism themes focused on in this design:

  • Strength — Elephants are renown for their size and with that size comes immense strength and power. So strength is the most obvious symbolism of the elephant. Consider that strength comes in many forms. It takes tremendous strength and power to sit quietly and clear our thoughts from our mind.
  • Good Luck — Many cultures associate the image of an elephant with its trunk up as good luck. In the Hindu religion, Ganesh takes the form of an elephant and is the lord of good fortune.
  • Mental Fortitude — Besides strength, Elephant’s are also known for their memory. It is said that when droughts come through their territories, elephants remember old watering holes from decades ago. Some people have even recorded elephants visiting grave sites of old friends and family members.
  • Community — Elephants are very social animals. They stand by their family and communities, which are matriarchal and consist anywhere from 8 to 100 individuals.
  • Gentle — For as powerful and big as elephants are they can be very precise and gentle with their movements through spaces and trunk dexterity.
  • Removing Obstacles — With their strength and gentle nature, elephants have been used to literally remove heavy obstacles from roads or for construction. Elephants are also associated with removing spiritual obstacles. Ganesh is also the remover of obstacles both physical and spiritual. How can you remove obstacles from your own life by being what you need to be when you need to be it?
  • Stability — Four powerful legs stand rooted. Massive muscle structures. Excellent balance and mobility.

Benefits of Warrior III

  • Strength — This posture works your entire body. From the top of your head to the tips of your toes. The key to warrior III pose is engaging your core, spine, and BOTH legs fully. The muscles in your feet, calves, and quads should be fully flexed. Now engage your core all around your stomach and back. And keep breathing WITH the posture. Inhales to lengthen your spine; reaching your leg and tip of your head in opposite directions. Then use your exhales to push down on the standing leg and rotate your pelvis parallel to the floor.
  • Mental Health — It is said that this pose improves memory and concentration. I think this may be connected to the amount of focus the posture requires. Perhaps there is something to be said about activating your entire core, spine, legs, and arms all at once and stretching everything in opposite directions for brain health. Citation needed; however, an interesting concept.

Affirmations in this Elephant Warrior III design

Here are all of the affirmations making up this Elephant Warrior III pose design:

·I am a remover of obstacles
·My path is clear
·I am powerful
·I am clever
·I am kind
·I am joyful
·I am strong
·I am gentle
·I am brilliant
·I am reliable
·I am stable
·I am patient
·I am dignified
·I am happy
·I am good luck
·I am fortunate
·I am grateful
·I am responsible
·I am sovereign
·I am steadfast
·I am sturdy
·I am a leader
·I am focused
·I am determined
·I am concentrating
·I am strong-minded
·I am breathing
·I am invigorating
·I am energized
·I am loyal
·I stand by my family, my friends, and my community
·I am involved
·I am alert
·I am a calming influence
·I am connected
·I am aware
·I am sensitive
·I am compassionate
·I charge through blockages
·I protect
·I remember
·I am forgiving
·I am effective
·I am social
·I am close
·I am providing
·I am harmonious
·I am beautiful
·I am majestic
·I am wise
·I am loved
·I am protected
·I love
·I am protecting
·I am intertwined
·I am balanced
·I am kindhearted
·I am mighty
·I am calm
·I am magnanimous

As well, here is the phrase at the bottom making up the yoga mat. We like to think of it as a strong foundation for life:

I am enjoying the journey. I am striving for excellence. I am breathing. I am smiling.

Conclusion

To sum it up, affirmations about the many meanings people all over the world and throughout human history assigned to the magnificent elephant make up this design. Elephant symbolism and Warrior III benefits are significantly overlapping in that they both relate to strength and mental fortitude. Therefore, when you are doing your warrior III pose, just imagine how much harder it would be if you were an elephant! And then remember that it doesn’t matter because you would still be getting the same benefits!

We currently screen print this Elephant Warrior III design on these items:
Elephant Warrior III

What are some of your favorite elephant symbolism ideas? What are your thoughts and tips on warrior III pose? Leave a comment and let us know!

Three Sided Breathing Technique

Use this Three Sided Breathing Technique anytime and anywhere to physically relax your body and calm your mind. The more we practice breathing exercises, the more likely we are to react with slow, deep breaths when we need to most!

The three sided breathing exercise is easy! Just visualize an equilateral triangle. All three sides are of equal length representing: inhaling, holding, and exhaling the breath for an equal amount of time. Note that unlike four sided breathing, there is no second ‘hold’ between the exhale and the inhale.

The goal is to make sure each side of the breath is equal when doing three sided breathing. If you pick 4 seconds but can only exhale for 2 seconds, then shorten all of the sides to two seconds and build up from there when you are ready.

Three Sided Breathing Technique

Follow along with the golden ring in this animated gif. Each side of the Three Sided Breathing exercise start at four seconds. Click on ‘Six Seconds’ or ‘Eight Seconds’ if you can do all three sides at four seconds and want to try more. Look below the image for further details and additional tips.




Three Sides of The Breath

Take a slow, deep INHALE through your nose right now. Fill your lungs completely and then push it all out. Take another breath filling from the bottom, from the diaphragm, all the way up to the top of your lungs. And push it all out. Now take a breath filling up your chest first and then continuing to inhale until your diaphragm is also full.

Inhaling should always be done through the nose to avoid getting a sore throat. Your nose is a natural filter.

Slow down that inhale to a trickle. Take complete control over the breath. Fill your lungs all the way.

HOLD the breath at the top. Feel the air in your body creating an internal pressure. Feel your heart beat perhaps.

Now, focus on your EXHALE. Push the air out from your diaphragm and empty your lungs completely. Squeeze all the air out of your chest. Feel the two movements and play with reversing the order. Breathe in and exhale from your chest then your diaphragm until all the air is out.

Put it all together. Make each side (Inhale, Hold, Exhale) the same length of time. You are doing three sided breathing!

Equilateral

When practicing three sided breathing always keep the three sides of the breath equal. Whether you do 1 second or 10 seconds a side it doesn’t matter. All that matters is that you are doing all three parts for an equal length of time. This will require you to control the flow of your breath; speeding it up or slowing it down as needed. I like to count out the seconds in my mind. They don’t have to be seconds just anything uniform.

Inhale…. 2…. 3…. 4…. Hold…. 2…. 3…. 4…. Exhale…. 2…. 3…. 4….

One more tip

To really experience the different ways you can inhale and exhale the breath, place one hand on your chest and the other on your stomach. Now take a deep breath in and out so that only one hand moves. Then do it again so that only the other hand moves. Lastly, put it together, breathe in so that one hand moves AND THEN the other hand until your lungs are all the way full and then empty.

Breathing Exercises and Meditation

Breathing exercises are not necessarily the same thing as meditation. But breathing exercises do make meditation a little easier by priming the mind and body to relax. Try using this three sided breathing technique 6-8 times and then go right into meditating. See if it makes a difference.

What do you think?

Leave a comment below to join the conversation. What do you think about this three sided breathing technique? What are your favorite breathing exercises?

San Diego Comic-Con 2017

We had the great fortune of going through the exhibit hall at San Diego Comic-Con 2017! Take a look at these photos to get a taste of what we saw 🙂

Whenever we get the chance to show someone our art made from tiny, positive words, we usually use the super power analogy… Using the right attitude in the right moment is like your super power for the day! So, keep in mind on some level you are already a super hero just waiting to spring into action with positive thinking.

Sea Turtle Design Made of Affirmations About Its Symbolism

Our Sea Turtle design is made completely out of tiny, positive affirmations relevant to turtle symbolism!

Here are some of the most prominent themes associated with sea turtles and turtles in general that we included in this design:

PROTECTION

A turtle’s most prominent and mesmerizing feature is its shell. A strong shell protects the turtle from most predators and hazards of life in the slow lane. Shelter is one of the universal principles for being a human being. The turtle carries its home with it wherever it goes symbolizing feeling at ease even in new surroundings. Being able to relax even in situations that would normally make us uncomfortable, like a job interview or handling a stressful but important task, is an ability that serves a positive thinker.

SLOWING DOWN

Turtles move slowly and breath slowly. There are times when urgency is important. There are other times when slowing down is the key to success. The turtles’ speed is renown for being slow and steady. Consistent and persistent eventually crosses the finish line. When we are hurrying through tasks we are prone to make more mistakes. When we move at our own pace, we are more likely to be successful. When it comes to tasks, the appropriate speed may always be changing as our abilities and techniques improve. However, when it comes to taking time for relationships and connecting with another, there is always benefit and space to slow down even more.

SET YOUR OWN PACE

Setting our own pace may be challenging at times. It is important to be aware of what pressures are attempting to get us to go at a different speed. Are they worthy? Or are we simply feeling rushed from outside pressures that are really about inside pressures? Like trying to impress someone else? The turtle always goes at its own pace. It sets the trend for those that want to jump on and ignores the trend of those that don’t. By being patient with ourselves we can allow ourself to move at the appropriate speed for the task at hand.

SUPPORT

With 4 strong legs, a wide base, and a low center of gravity, turtles are known for their sturdy nature and relative strength. Many cultures look to the turtle as as symbol of support and a strong foundation. Several cultures hold beliefs that involve a turtle supporting the entire world on its back. It is known as the Cosmic Turtle, World-bearing Turtle, or Great Turtle. The turtle will not let you down. It will help guide you safely to where you are going. How can you tap into this truth about yourself to support someone else in some way today?

PEACEMAKERS

Moving at a slow, steady pace is associated with tranquility and peace. Making peace implies changing war-like energy and requires slow, careful planning and persistent movement towards the end goal. Turtle symbolism implies strength used to carry the armor shell and therefore implies protection. As compared to say a Lion who’s strength is used to drive fangs and claws in attack. From a strong protected state and with steady persistence. Some Native American cultures look to turtles as symbols of the peace-maker.

GOOD LUCK / GOOD FORTUNE

In many human societies throughout time you will find a Turtle associated with good luck and good fortune. In several mythologies a turtle either created the Earth, supports the Earth, or saved the day from a disaster like a flood. The notion of being protected seems intertwined with having good luck.

GOOD HEALTH

Beyond the association between having good luck and protection with good health; turtles have other connections to this positive ideal as well. They live on average for 100 years and can live up to 150 years which specifically ties turtles symbolism to longevity and in turn good health. On a grimmer note turtle shells were commonly used to mix medicines and turned into musical shakers for spiritual dances. This is in part why turtles are associated with mystical and spiritual symbolisms.

GROUNDED

Turtle symbolism comes back to the stories from many cultures that turtles helped create the world and/or support it. Called the Cosmic Turtle, World-bearing Turtle, or Great Turtle, the turtle is associated with Mother Earth, creation, being grounded, and connectivity.

See this design on a women’s tank top: CLICK HERE

Here are all of the affirmations we used to make this turtle design. Each one rotates through the expansion of “I am”, “You are”, and “We are” statements.

They are all true about you. We have all been all of these truths before and can be them again. Hopefully, the perfect ones jump out at you at the perfect moment 🙂

Affirmations used in our Sea Turtle Design

·You are adapting.
·You are lucky.
·We are walking gently.
·You are safe.
·We are strong.
·I am making peace.
·You are understanding.
·You are strong.
·You are a peacemaker.
·We are overcoming.
·We are gentle.
·We are organizing.
·You are patient.
·I face the unknown.
·You are creating.
·You are succeeding.
·You are in order.
·We are kind.
·You are comfortable.
·We are healing.
·I am grounded.
·You are leading.
·You are calm.
·You are free.
·We are supporting.
·We are peacemakers.
·You are supporting.
·We are guided.
·You are gentle.
·You are the world.
·I am adapting.
·I am fertile.
·You are happy.
·We are given safe passage.
·We are proceeding.
·We are connected.
·I am fortunate.
·You are innocent.
·I am supported.
·You are steady.
·We are supported.
·We are navigating.
·We are purposeful.
·I am blessed.
·I am resolute.
·I am free.
·We are setting the pace.
·We are looking within.
·You are connected.
·We are pacing ourselves.
·We are in order.
·I am walking gently.
·We are finding.
·You are walking gently.
·We are innocent.
·We are adapting.
·We are free.
·I am finding.
·You sustain.
·You are capable.
·We are healthy.
·I am guided.
·I am continuing.
·You are trusting.
·We are resolute.
·I am looking within.
·I am persistent.
·I am enduring.
·We are gliding.
·I sustain.
·I am resilient.
·I am kind.
·You are floating.
·We are protecting.
·We are home.
·You are guided.
·You are kind.
·You are on course.
·I am happy.
·You are eternal.
·I am understanding.
·I am gentle.
·We are creating.
·I am healing.
·I am slowing down.
·We are carrying on.
·We are determined.
·We are happy.
·I am peaceful.
·I am the world.
·We are resilient.
·I am on course.
·I am steadfast.
·You are home.
·You are grounded.
·You are protected.
·We face the unknown.
·I am pacing myself.
·We are understanding.
·You are protecting.
·We are safe.
·You are at ease.
·You are ready.
·You are fertile.
·We are protected.
·I am trusting.
·I am strong.
·You are stable.
·We are comfortable.
·We are lucky.
·You are traveling.
·I am a peacemaker.
·I am protecting.
·We are good luck.
·You are overcoming.
·You are given safe passage.
·You are looking within.
·We are the world.
·I am good luck.
·You are adaptive.
·You are slowing down.
·You are setting the pace.
·I am eternal.
·You are fit.
·We are self paced.
·I am connected.
·We are grounded.
·I am safe.
·I am at ease.
·You are resolute.
·You are proceeding.
·I am leading.
·I am supporting.
·We are steady.
·We are persistent.
·You are steadfast.
·We are peaceful.
·You are enduring.
·I am proceeding.
·I am setting the pace.
·We are fit.
·I am steady.
·We are calm.
·We are stable.
·I am sure.
·I am calm.
·We are making peace.
·I am in order.
·I am lucky.
·We are succeeding.
·I am floating.
·We are slowing down.
·You are healthy.
·We are continuing.
·I am ready.
·You are true.
·We are on course.
·You are finding.
·You are blessed.
·We are steadfast.
·We are floating.
·You are healing.
·We sustain.
·We are blessed.
·You are carrying on.
·You are resilient.
·You face the unknown.
·I am protected.
·We are true.
·You are gliding.
·I am given safe passage.
·I am healthy.
·I am patient.
·We are ready.
·You are peaceful.
·I am home.
·I am capable.
·You are wise.
·I am creating.
·You are organizing.
·I am determined.
·I am self paced.
·I am organizing.
·You are supported.
·You are persistent.
·You are purposeful.
·You are surviving.
·We are adaptive.
·You are making peace.
·We are surviving.
·You are navigating.
·I am innocent.
·I am true.
·I am adaptive.
·I am comfortable.
·I am wise.
·We are capable.
·You are continuing.
·You are sure.
·We are leading.
·We are fortunate.
·We are enduring.
·I am carrying on.
·We are fertile.
·I am overcoming.
·I am fit.
·We are at ease.
·I am traveling.
·I am navigating.
·We are patient.
·I am surviving.
·I am gliding.
·I am purposeful.
·We are trusting.
·We are traveling.
·You are self paced.
·We are wise.
·You are fortunate.
·I am stable.
·You are determined.
·You are good luck.
·We are eternal.
·We are sure.
·I am succeeding.
·You are pacing yourself.