Bilva tree and lord shiva

Bilva Patra Tree B/h. Nilkanth Mahadev (300 Years Old), Hirapur.
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Bilva tree . isha.sadhguru.o
Bilva leaves are dear to Lord Shiva or Mahadeva and they have close links with Mahalakshmi, the consort of Lord Vishnu. Bilva tree (in Tamil: Vilvamaram) is sacred to the Hindus and  Bilva tree(s) is grown  in
all major shiva temples.  Besides Lakshmi, Goddess Parvati, Goddess Gauri live in this sacred tree. Bilva leaves are widely used by the priests for temple ritual and prayers, particularly when chanting mantras in Sanskrit. This practice has been in vogue for several centuries. The tree, being holy and dear to Lord shiva, the dry  trunk should not be cut to pieces and used as fuel. The Santhal tribes of Northern  India worship the tree stumps and offer prayers. Hindus believe  that our Karma will get considerable relief  if Bilva leaves are offered to the Shiva Linga - a way of reducing our sins committed knowingly or un-knowingly. The trifoliate form of leaves symbolize the trident that Shiva holds in his right hand.
Bael leaves used in worship of a lingam - icon of Shiva.en.wikipedia.org/

Bilvapatra contains 2% Shiva tatva. By offering bilvapatra to the Shivpindi on Mahashivratri, the manifest Shiva tatva near the stalk of the bilvapatra getsspeakingtree.in

Trees  are  mentioned  in  many of  the  world's mythologies  and  religions,  and  have  been  considered sacred  throughout the ages. The Yule Tree in Germanic mythology, the Tree of Knowledge of Judaism and Christianity, the  Bodhi  tree  in Buddhism and  Saglagar  tree in  Mongolian Tengriism  are  worth  mentioning. There is close similarity between the life cycle of humans and that of trees  and they represent a powerful symbol of  growth. death and rebirth. The growth, the annual death and revival of their foliage, make the trees stand apart.  Evergreen  rees  such  as  Banyan, Peepal, etc that remain  green throughout these cycles, are sometimes considered symbols  of  the eternal, immortality or fertility. 
Bilva leaf .kinkars.blogspot.com
The Bilva tree or Bael ( Aegle  Marmelops) tree grows in many parts of India under different tropical and soil conditions. Bael tree can sustain different temperatures, PH values of soil and can grow where no other trees take life. Bael fruit taste like citrus fruit The tree is characteristic of tall growth with strong rough trunk and thorny in nature. Besides Shiva temples, Bilva leaves are used for the worship of Goddess Durga  or  Kali.  Prana Prathistha  is performed using  Bilva leaves by chanting certain mantras by the priest. It simply means energizing or transferring life force to the idol. Once the process 
is  complete,  energy  is  released  called Visarjan.
Bilvapatra personifies Shiva tatva.  offering bilvapatra to the Shivpindi on Mahashivratri is a sacred duty.,  Shiva tatva - the stalk of the bilvapatra getswww.icmag.com
Bilva has high medicinal values. Leaves, roots and fruits are used for ayurvedic medical preparations to treat may ailments.  Bael fruit tastes like citrus 
fruit  and is rich in vitamin C. Single Bilva  leaf  is  a combination of three or five or seven leaflets.

Belpatra, (Bilva), according to the scriptures and Ayurveda, has great medicinal values and is quite beneficial for health.  Bilva leaf's  trifoliate  shape represents the three  Gunas, namely Sattva, Rajas and Tamas that define a person's personality. The Sattva guna  stands for  positive energies and lodges in the center of the leaf, while  the Tamas is the negative forces. So, when a person is dejected and depressed, he is  affected by negative energies. When such a person, it is believed, touches the Belpatra, the positive energies are transferred to him/her.
 In an Ekabilvam - single trifoliate bel-patra, Left leaf is Brahma, Right leaf is Vishnu and the middle leaf is Shiva.

With respect to Shiva pooja, besides other ritualistic formalities, offering Bilva leaves is considered to be the most sacred  practice. A true devotee should offer only trifoliate - three inseparable leaves called Bila dalam. it is not advisable to offer incomplete  Bel -Patra.

The trifoliate leaves of Bilva represent the form of Shiva  and also various characteristics of human beings as well. The three faces of a leaf represent the following:  01. Three eyes of  Lord Shiva, the third eye being Gnakkann- eye of wisdom, 02. Brahma, Vishnu and Maheswara - the three forms or Swaroopa, 03. Three syllables of Aumkara (Omkara) - Akara, Ukara  and  Makara. One can get rid of darkness caused due to agyanam / ignorance), 04. Bilva dalam represents Srusthi (Creation), Sthithi (Sustaining) and Laya (dissolution),  05. Pooja, Stotra and Gyana, 06. Bilva leaves add positive energy and one  can get rid of negative thoughts.

Ref:
https://en.wikipedia.org/wiki/Trees_in_mythology