Significance of the Fibonacci sequence

The Fibonacci sequence serves as a bridge between mathematics and the natural world, illustrating fundamental patterns of growth and arrangement that recur across various forms of life. Understanding these patterns not only enriches our appreciation of nature but also aids in fields like biology, ecology, and even arts.

The Fibonacci sequence, a series of numbers where each number is the sum of the two preceding ones (usually starting with 0 and 1), has profound significance in understanding nature due to its frequent appearance in various biological settings.

The Fibonacci sequence is 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, the zeroth Fibonacci number is 0, the first Fibonacci number is 1, and every later Fibonacci number is the sum of the two previous Fibonacci numbers. The sequence is named after Leonardo of Pisa, who described them in his arithmetic book Liber Abaci in 1202 using a cute story about breeding rabbits, and who was given the nickname “Fibonacci” about 600 years after his death.

Fibonacci sequence = 0, 1, 1, 2, 3, 5, 8, 13, 21,

Here, third term “1” is obtained by adding the first and second terms. (i.e., 0+1 = 1)

Similarly, “2” is obtained by adding the second and third terms (1+1 = 2)

“3” is obtained by adding the third and fourth terms (1+2) and so on.

The ratio of each Fibonacci number with the preceding Fibonacci number is called the Golden Ratio or Phi. For example: 13/8 = 1.625, 21/13 = 1.615, 34/21 = 1.619, 55/34 = 1.618, 89/55 = 1.618, etc. Golden Ratio (ɸ)

There are many things in which Fibonacci series are followed.

Some of them are:-

1.    Flower Petals

The number of petals in a flower consistently follows the Fibonacci series. Examples include the lily, which has three petals, buttercups, which have five the chicory's 21, the daisy's 34, and so on.

2. Seed Heads

The head of a flower is also subject to Fibonacci series. Typically, seeds are produced at the center, and then migrate towards the outside to fill all the space. Sunflowers provide a great example of these spiraling patterns.

3. Pinecones

The seed pods on a pinecone are arranged in a spiral pattern. Each cone consists of a pair of spirals, each one spiraling upwards in opposing directions. The number of steps will almost always match a pair of consecutive Fibonacci numbers.

4. Fruits and Vegetables

Spiraling patterns can be found on pineapples and cauliflower.

5. Tree Branches

The Fibonacci sequence can also be seen in the way tree branches form or split. A main trunk will grow until it produces a branch, which creates two growth points. Then, one of the new stems branches into two, while the other one lies dormant. This pattern of branching is repeated for each of the new stems. A good example is the sneezewort.

6. Shells

The unique properties of the Golden Rectangle provides another example. This shape, a rectangle in which the ratio of the sides a/b is equal to the golden mean (phi), can result in a nesting process that can be repeated into infinity — and which takes on the form of a spiral.

7. Space Galaxies

Spiral galaxies also follow the familiar Fibonacci pattern. The Milky Way has several spiral arms, each of them a logarithmic spiral of about 12 degrees.

8. Hurricanes

The properties of Golden Rectangle provides another example.

9. Faces

Faces, both human and nonhuman, abound with examples of the Golden Ratio. The mouth and nose are each positioned at golden sections of the distance between the eyes and the bottom of the chin. Similar proportions can been seen from the side, and even the eye and ear itself.

10. Fingers

Looking at the length of our fingers, each section — from the tip of the base to the wrist — is larger than the preceding one by roughly the ratio of phi.

So these are the 10 things in which Fibonacci series is followed.

There are many more! It is easy to find Fibonacci series in plant life. Flower structures, whirling of leaves in stems, leaf development and unfolding (ESP. In ferns), and seed placement in composite flower are all evident Fibonacci series.

We often miss them because we are not looking for the pattern or, as is often the case, the act of living comes with risks of damage and alteration by wind, weather, and people with pruning shears.

The spiritual meaning of the Fibonacci spiral is often associated with balance,harmony, and perfection. Some believe that this pattern represents the infinite and interconnected nature of all things. It symbolizes the natural order and balance found in the universe and signifies the beauty and efficiency of creation. Its perfect symmetry and infinite sequence reflect the harmonious nature of the universe.

Personal and Spiritual Growth through the Spiral

Visualizing life as a spiral encourages seeing each experience as a step toward higher potential.

Setting intentions aligned with the spiral’s balance supports harmonious manifestation of desires.

Regular meditation on the spiral deepens connection to universal energies and fosters a sense of belonging.

YOGA IN RAINY SEASON

Monsoon yoga can be an excellent tool for those looking for a health boost during the rainy season. Regular yoga can boost immunity, helping to ward off seasonal illnesses that are more prevalent during the monsoon. Yoga improves immunity, boosts flexibility, and reduces stress during the dull, dreary days of monsoon.

Monsoon yoga offers a unique opportunity to deepen your practice while connecting with the seasonal changes around you. Embrace the rains, find joy in your practice, and enjoy the benefits of this refreshing season.

The only downside to the rainy season is the physical dullness it brings along, which makes it difficult to go through the day without wanting to take a nap or two. A dedicated yoga routine can play a vital role in improving energy levels and keeping you active and alert throughout the day. 

Yoga poses that focus on groundings, such as mountain poses or tree poses, can help individuals feel more rooted and stable during the sometimes turbulent energy of the monsoon season.

Monsoon Yoga Poses and Pranayama

These simple pranayama and yoga poses will equip you against monsoons’ grim side-effects:

Kapal Bhati pranayama

Nadi Shodhan pranayama

Adho Mukha Svanasana

Setu Bandh asana

Bhujangasana

Naukasana

Tips for Indoor Yoga:
1. Create a Peaceful Space:
- Choose a quiet, well-ventilated area for your practice.
- Use a yoga mat with good grip to prevent slipping.
2. Stay Hydrated:
- Keep water nearby to stay hydrated and counteract the effects of humidity and sweat.
3. Adapt Your Routine:
- Focus on Asanas that improve circulation and relieve stiffness, such as Tad asana (Mountain Pose) and Vrikshasana (Tree Pose).
- Incorporate calming, cooling postures like Shavasana (Corpse Pose) to help balance the body's energy.
4. Breathing Techniques:
- Practice Pranayama to enhance lung capacity and purify the respiratory system, which is particularly beneficial during the damp monsoon season.
5. Mindfulness and Meditation:
- Utilize the sound of rain as a natural aid in meditation to deepen relaxation and focus.
6. Maintain Cleanliness:
- Ensure your practice space remains dry and clean to prevent mold and mildew buildup.
7. Incorporate Props:
- Use yoga blocks or straps to support stability and flexibility, especially if the increased humidity makes movements more challenging.

The monsoon isn’t something to avoid. It’s nature’s gift for deeper healing. When the rains come to India, they don’t just nourish the earth; they create the perfect conditions for human rejuvenation too.

भगवान श्रीकृष्ण के 28 नाम

श्रीमद्भागवत के अनुसार–’भगवान का नाम प्रेम से, बिना प्रेम से, किसी संकेत के रूप में, हंसी-मजाक करते हुए, किसी डांट-फटकार लगाने में अथवा अपमान के रूप में भी लेने से मनुष्य के सम्पूर्ण पाप नष्ट हो जाते हैं ।’

हरे कृष्ण मंत्र है:

हरे कृष्ण हरे कृष्ण कृष्ण कृष्ण हरे हरे

हरे राम हरे राम राम राम हरे हरे ||

अर्थ- श्री कृष्ण और भगवान राम को प्रणाम। वे दो शरीर हैं लेकिन श्री हरि विष्णु के अवतार होने के कारण दोनों एक ही हैं।

श्रीकृष्ण और अर्जुन संवाद

एक बार भगवान श्रीकृष्ण से अर्जुन ने पूछा—‘केशव! मनुष्य बार-बार आपके एक हजार नामों का जप क्यों करता है, उनका जप करना तो बहुत ही श्रम साध्य है । आप मनुष्यों की सुविधा के लिए एक हजार नामों के समान फल देने अपने दिव्य नाम बताइए ।’

भगवान श्रीकृष्ण ने कहा—‘मैं अपने ऐसे चमत्कारी 28 नाम बताता हूँ जिनका जप करने से मनुष्य के शरीर में पाप नहीं रह पाता है । वह मनुष्य एक करोड़ गो-दान, एक सौ अश्वमेध-यज्ञ और एक हजार कन्यादान का फल प्राप्त करता है । अमावस्या, पूर्णिमा तथा एकादशी तिथि को और प्रतिदिन प्रात:, मध्याह्न व सायंकाल इन नामों का स्मरण करने या जप करने से मनुष्य सम्पूर्ण पापों से मुक्त हो जाता है ।’ 

समस्त पापनाशक भगवान के 28 दिव्य नामों का स्तोत्र (श्रीविष्णोरष्टाविंशति नाम स्तोत्रम्)

अर्जुन उवाच!

किं नु नाम सहस्त्राणि जपते च पुन: पुन: ।
यानि नामानि दिव्यानि तानि चाचक्ष्व केशव ।।

श्रीभगवानुवाच

मत्स्यं कूर्मं वराहं च वामनं च जनार्दनम् ।
गोविन्दं पुण्डरीकाक्षं माधवं मधुसूदनम् ।।
पद्मनाभं सहस्त्राक्षं वनमालिं हलायुधम् ।
गोवर्धनं हृषीकेशं वैकुण्ठं पुरुषोत्तमम् ।।
विश्वरूपं वासुदेवं रामं नारायणं हरिम् ।
दामोदरं श्रीधरं च वेदांगं गरुणध्वजम् ।।
अनन्तं कृष्णगोपालं जपतोनास्ति पातकम् ।
गवां कोटिप्रदानस्य अश्वमेधशतस्य च ।।

भगवान श्रीकृष्ण के 28 दिव्य नाम (हिन्दी में)

1.  मत्स्य

2.  कूर्म

3.  वराह

4.  वामन

5.  जनार्दन

6.  गोविन्द

7.  पुण्डरीकाक्ष

8.  माधव

9.  मधुसूदन

10.     पद्मनाभ

11.     सहस्त्राक्ष

12.     वनमाली

13.     हलायुध

14.     गोवर्धन

15.     हृषीकेश

16.     वैकुण्ठ

17.     पुरुषोत्तम

18.     विश्वरूप

19.     वासुदेव

20.     राम

21.     नारायण

22.     हरि

23.     दामोदर

24.     श्रीधर

25.     वेदांग

26.     गरुड़ध्वज

27.     अनन्त

28.      कृष्णगोपाल

जीवन की जटिलताओं में फंसे, हारे-थके, आत्म-विस्मृत सम्पूर्ण प्राणियों के लिए आज के जीवन में भगवन्नाम ही एकमात्र तप है, एकमात्र साधन है, एकमात्र धर्म है । इस मनुष्य जीवन का कोई भरोसा नहीं है । इसके प्रत्येक श्वास का बड़ा मोल है । अत: उसका पूरा सदुपयोग करना चाहिए ।

श्रीकृष्ण के हर नाम में प्रेम, दया और ज्ञान की गहराई है। ये नाम उनके गुणों की झलक मात्र हैं। इनमें से आपका पसंदीदा नाम कौन-सा है? साथ में यह भी अवश्य बताएं कि आपके लिए वे क्या हैं — एक मार्गदर्शक, एक प्रेमी, एक गुरु या जीवन का सार? कमेंट में जरूर बताएं!

जय श्रीकृष्ण!

Live a #Yoga lifestyle.

Use your oxygen – You might find that using oxygen when you do Yoga makes a beneficial difference. You can be more active and have less worry.

A lifetime of living out of alignment, both physically and mentally, creates postural imbalances in our musculoskeletal system that strain our joints, limit our movement, and cause pain. Chronic stress leads to adrenal fatigue and physical changes in our hearts and minds. The memory of unresolved trauma and emotion works its way into our cells and connective tissues.  Yoga offers pushes and pulls on the body in such a way that it realigns us physically and mentally. Yoga is unlike other fitness movements in that it goes beyond strength building, flexibility or weight loss. Yoga brings calm and clarity to the mind by healing the body.

After beginning yoga, you may start to see physical changes to your body, like

• Better posture
• Muscle toning;
• Improved mobility

• You feel more relaxed, both mentally and physically.
• You’re refreshed and ready to take on the rest of your day.
• You’re less tense.
• Your joints feel loose and your muscles feel well-worked.

And you might notice a mental switch, too, like:

• Decreased stress levels
• More energy; or
• Better cognition and focus.

Before Yoga: Stiff, tired, stressed, maybe some aches and low energy.

After Yoga: More flexible, stronger, relaxed, better posture increased energy, and a calmer mind.

It’s like upgrading your body and mind—inside and out!

Yoga can make you flexible, increase your metabolism, stimulate all sorts of glands, and tone and clean your internal organs. It can also give you clam and mental poise. Yoga is for the mind. Yoga is a way of living a good life. You will experience a sound sleep.

After doing it for few days you will feel more energetic all the day with brighter mood.

It helps to boost your immunity also.

Hope above is enough for you to start the yoga.

Remember that progress takes time, so embrace the journey and enjoy the positive changes that yoga brings to your body shape.

Raise levels of happiness.

Happiness is a feeling or state of well-being and contentment.

The Happiness Index is a comprehensive survey instrument that assesses happiness, wellbeing, and aspects of sustainability and resilience.

Domains of Happiness - The Happiness Index measures life satisfaction, the feeling of happiness, and other happiness domains: psychological well-being, health, time balance, community, social support, education, arts and culture, environment, governance, material well-being, and work.

● Psychological Well-Being: optimism, senses of purpose and of accomplishment;

● Health: energy level and ability to perform everyday activities; 

● Time Balance: enjoyment, feeling rushed, and sense of leisure;

● Community: sense of belonging, volunteerism, and sense of safety; 

● Social Support: satisfaction with friends and family, feeling loved, and feeling lonely;

● Education, Arts, and Culture: access to cultural and educational events and diversity; 

● Environment: access to nature, pollution, and conservation;

● Governance: trust in government, sense of corruption, and competency;

● Material Well-Being: financial security and meeting basic needs; and

● Work: compensation, autonomy, and productivity. (Happiness Alliance, 2014c)

As per the report of the World Happiness Index in the year 2021, here are the world’s happiest countries:

1.       Finland.

2.      Denmark.

3.     Switzerland.

4.     Iceland.

5.     The Netherlands.

6.     Norway.

7.     Sweden.

8.     Luxembourg.

9.     New Zealand.

10. Austria.

Role of Gyri and Sulci in improving happiness

Gyri (ridges) and sulci (grooves) on the brain's surface are crucial for cognitive function and happiness, not directly by improving happiness, but by enabling the brain to process information more effectively and create a foundation for mental well-being. They increase the brain's surface area, allowing for more neurons to be packed into the cortex, and they form divisions and boundaries within the brain.  They are essential for creating a brain environment that supports efficient information processing, healthy neurotransmitter regulation, and overall cognitive function, all of which contribute to a sense of well-being and happiness. 

Ø Increasing happiness in your life:

Ø Focus upon problem-solving, not just venting

Ø Take time to build quality relationships with supportive people

Ø Count your blessings and practice gratitude

Ø Take time to engage in random acts of kindness

Ø Respond actively and constructively, celebrating when others share good news with you

Ø Attend to others mindfully, and practice compassion and empathy

Ø Be kind to yourself, rather than overly self-critical or perfectionistic

Ø Savor experiences because this will intensify and prolong your enjoyment of them

Ø Set meaningful goals for yourself that provide structure and purpose, give a sense of identity and increase self-esteem

Ø Build intrinsic motivation, rather than just relying upon doing things to please others 

Ø Seek healthy challenges, stretching your abilities just a bit beyond your comfort zone to realize your potential

Ø Appreciate what you already have rather than focusing only upon what you still desire

Ø Avoid the temptation to complain and reinforce negativity; instead, cultivate optimism and practice positively reframing your circumstances

Happiness can vary from one person to the next. It involves a balance between momentary pleasure and longer-term striving toward goals. 

The Buddhist definition of “happiness” is the state of mind of contentment, satisfaction, inner peace, serenity, and joy, which comes from eliminating all the negative feelings and thoughts which irritate us, like anger hate, rage, jealousy, fear, worry, restlessness, Envy, lust, and craving.

It's very easy to be happy, but we search happiness in the wrong places.

We think happiness comes from the best, but the fact is that-

“Happinessis a beautiful flower which grows out of the seeds of simplicity, in the ground of nothingness, fed with indifference towards circumstances”

Everyone strives hard to be happy in life because each and every person deserves to be happy. It is not impossible to gain happiness but consistent effort should be made to achieve goals which in turn makes one happy. Find reasons to be happy and avoid reasons to be sad, learn to tame your mind because you are not its servant.

I would really recommend these books to anyone. These books are very different.

1)   SELF – HEALING REGIMEN …… from illness to wellness

2)   DOSE – The happy brain chemicals.

“Don't hope for a life without problems. There's no such thing. Instead, hope for a life full of good problems”