The number π is a mathematical constant, the ratio of a circle's circumference to its diameter, approximately equal to 3.1415926. It has been represented by the Greek letter "π" since the mid-18th century and it is commonly spelled as "pi."
Pi - π - is a so called irrational number and cannot be expressed exactly as a common fraction. Consequently its decimal representation never ends and never settles into a permanent repeating pattern. The digits appear to be randomly distributed although no proof of this has yet been discovered. Also, π is a transcendental number – a number that is not the root of any nonzero polynomial having rational coefficients. This transcendence of π implies that it is impossible to solve the ancient challenge of squaring the circle with a compass and straight-edge.
For thousands of years mathematicians have attempted to extend their understanding of π, sometimes by computing its value to a high degree of accuracy. Before the 15th century mathematicians such as the Greek Archimedes and the Chinese Liu Hui used geometrical techniques, based on polygons, to estimate the value of π. Starting around the 15th century, new algorithms based on infinite series revolutionized the computation of π. In the 20th and 21st centuries mathematicians and computer scientists discovered new approaches that, when combined with increasing computational power, extended the decimal representation of π to, as of late 2011, over 10 trillion (1013) digits. Scientific applications generally require no more than 40 digits of π
so the primary motivation for these computations is the human desire to
break records but the extensive calculations involved have been used to
test supercomputers and high-precision multiplication algorithms.
Because its definition relates to the circle π is found in many formulae in trigonometry and geometry,
especially those concerning circles, ellipses or spheres. It is also
found in formulae used in other branches of science such as cosmology, number theory, statistics, fractals, thermodynamics, mechanics and electromagnetism. The ubiquity of π
makes it one of the most widely-known mathematical constants both
inside and outside the scientific community: Several books devoted to it
have been published, the number is celebrated on Pi Day and record-setting calculations of the digits of π often result in news headlines. Attempts to memorize the value of π with increasing precision have led to records of over 67,000 digits.
If mathematics is not exactly your forte, maybe cooking is. All over the United States people celebrate π with an ever increasing number of pie recipes.
The Shepherd's Pie recipe comes from Williams-Sonoma blog taste and makes an excellent use of leftover short ribs which probably is a rare, but probable occurrence.
4 beef short ribs, each 2 1/4-2 1/2 lb.
Sea salt and ground pepper
2 Tbs. extra-virgin olive oil
1 large onion, chopped
2 celery stalks, chopped
6 cloves garlic, crushed
1 carrot, chopped
3 1/2 cups dry red wine, such as Syrah
3 bay leaves
1 Tbs. fresh thyme leaves
4 cups beef stock, or as needed
1 1/2 lb. Yukon gold potatoes, peeled and quartered
1/4 cup milk
4 Tbs. unsalted butter
1 egg yolk, beaten
Season ribs with salt and pepper and refrigerate for at least 6 hours or
up to overnight. Bring to room temperature and season again with salt
Preheat oven to 350 degrees F. Heat a large saute pan over high heat
until hot. Add olive oil and heat until shimmering. In batches, sear
ribs on all sides, turning as needed, until well browned. Transfer to a
Dutch oven. Pour off all but 2 tablespoons fat from saute pan and return
to medium heat. Add onion, celery, garlic and carrot and saute until
beginning to caramelize, about 5 minutes. Add wine, bay leaves and
thyme, raise heat to medium-high, and boil to reduce wine by half. Add
stock, bring to a boil, and pour contents of pan over ribs. They should
be just covered with liquid; add stock as needed.
Cover tightly and braise in oven, adding stock as needed to maintain
liquid level, until a fork slides easily through meat, about 2 1/2
hours. Skim off any fat from surface, let ribs cool in liquid until they
can be handled, then remove ribs from pot and pull meat from bones.
Shred meat into bite-sized pieces, return to Dutch oven, and discard
While ribs are cooling, in a saucepan, cook potatoes in boiling
salted water until tender, about 15 minutes. Drain, dry in pan over low
heat, then pass through ricer back into warm pan. In a small saucepan,
heat milk and butter until mixture is steaming. Pour into potatoes, add
egg yolk and fold to mix well.
Raise oven temperature to 400 degrees F. Transfer contents of Dutch oven
to a 9-by-13-inch baking dish or divide among individual gratin dishes.
Cover top(s) evenly with potatoes. Bake until topping is golden, 35-40
minutes. Serve at once and enjoy! Serves 6-8.
Last year my Spanish neighbor Miranda told me
that she was diagnosed with cancer. Her kidneys were infested with
tumors and she had six to nine months to live if she underwent the
classical anti-cancer therapy that included chemotherapy, surgery and
radiation. Her two sisters and a younger brother had the same disease and did not make it. Miranda is a diminutive, good-natured lady in her mid-fifties. The
diagnosis did not change much of her outlook on life. A Spanish Catholic
she decided to put her life into God's hands and was playing with the
idea of dying without allowing the horrible chemotherapy to destroy her.
Miranda is a lucky lady. She has at
least three natural health "obsessed" neighbors: a therapeutic masseur
and at least two herbal medicine aficionados, one of those using
graviola on regular bases as an "insurance" against cancer.
I see Miranda from time to time, but do not have the courage to ask
about her disease. She still has her wonderfully thick hair and does not
look incredibly sick. In fact, it seems to me that she is somewhat
improving. And always smiling!
Another neighbor told me that Miranda decided to change her lifestyle.
She decided to detoxify her body and change her nutrition just a bit to
begin with. She also works with the masseur next door. She undergoes a
massage therapy to calm her nerves and reduce the stress. And, after the
herbs-loving neighbor made a suggestion, she is now on graviola for
almost five months. The best thing is, her tumors disappeared completely
and she is in no need of any conventional anti-cancer treatment!
Each cancer case is individual, each immune system reacts differently to
stimulation, but Miranda is the first person I have ever met who
recovered from cancer with natural means. For years I kept graviola and few other nature wonders in the back of my
mind for the horrible eventuality. If I were ever to be diagnosed with
cancer this would be what I would opt for. Knowledge may save your life,
I told myself years ago. It can save the lives of others if you share
it with them. This is what the other neighbor did and saved Miranda a
lot of pain. I checked the Internet and found that graviola is surrounded by
controversy and I advise caution when you decide to use it a s a cure.
But one thing must be said, graviola was used by native people of South
America to cure many ailments and can be still used to improve one's
immune response. Like with any product on the market you must consider
the purity of the product and the real content of the herb before you
buy a supplement.
~ Health Benefits of Graviola ~
Graviola (Annona muricata), also known as soursop, is an evergreen plant
native to Central and South America. It grows in Mexico, Cuba, the
Caribbean, Colombia, Brazil, and Venezuela, among others. Graviola is
also cultivated in parts of Africa and in Southeast Asia.
Graviola plant produces fruits with edible white pulp and indigestible
black seeds. The fruit pulp is used to make smoothies, juices and
The fruit is rich in Vitamin C; B vitamins including B1, B2, B3, B5, B6
and folate; minerals including calcium, magnesium, potassium,
phosphorus, iron, and zinc; and choline.
Indigenous natural medicine uses all parts of the graviola plant: fruit,
bark, leaves, roots, and seeds, and attributes different healing
properties to each. The fruit, for instance, is used to rid the body of the intestinal
parasites and worms. It is also used to bring dawn the fever, increase
mother's milk after childbirth, cure diarrhea and dysentery. The bark,
leaves and roots are used as infusion that is considered to be
anti-spasmodic, hypotensive and sedative. Crushed seeds of the fruit are
used against internal and external parasites, including worms and head
lice. A tea made of leaves is used to control diabetes, strengthen the
liver, and calm the inflammation of the mucosa.
Graviola contains many active compounds that have been studied by
scientists since the 1940s. Of great interest to scientists is the group
of chemicals called Annonaceous acetogenins. Graviola produces these
compounds in its leaves, stem, barks and seeds. Three independently
conducted studies demonstrated that these compounds have significant
anti-tumor properties and selective toxicity against various cancer
cells without harming the healthy cells in the body. Many of these
acetogenins were selectively toxic to cancer cells at a very law doses.
Studies published in 1998 describe active compounds in graviola as
having strong anti-tumor, anti-cancer, anti-viral and anti-parasitic
properties. While ongoing studies produce even more promising results, there are
some who dismiss graviola claiming that there is no successful research
proving graviola's efficacy against cancer. Moreover, inferior graviola
products are being sold all over the Internet and spectacular claims are
being made without much justification by people who take advantage of
those who suffer from cancer.
Like any herb, graviola does not come without side effects and
contra-indications. Graviola should not be taken by pregnant women,
people with law blood pressure. Since graviola is a potent
anti-microbial agent, it can kill off the friendly bacteria in the gut.
Supplementation with probiotics may be necessary with prolonged use of
No interaction with pharmaceutical drugs has been reported so far, but
since graviola is a cardio-depressant and vasodilator, it may potentiate
anti-hypertensive and cardiac depressant drugs. Supplementation with CoQ10 during the graviola therapy may render
graviola supplements less effective. CoQ10 increases levels of ATP.
Graviola, on the other hand, blocks transfer of ATP to cancer cells. ATP
(adenosine triphosphate) is a primary source of intracellular energy.
In order to survive, reproduce and grow, a cancer cell needs large
amounts of energy. When acetogenins in graviola block the energy flow to
a cancer cell, it can no longer grow and is destined to die.
Some alkaloids extracted from the seeds and roots of graviola are
neurotoxic and may cause neuronal dysfunction and degeneration leading
to symptoms of Parkinson's disease. Their use is not recommended.
Many cancer patients and health practitioners using extracts from leaves
and stem of graviola as a complimentary therapy in their cancer
protocols. The suggested therapeutic use is 2000-3000 mg to be taken
three times a day.
Contact certified health care provider, certified herbalist or certified
nutritionist before you choose self medication with graviola supplements.
By Dominique Allmon
*This information is for educational purpose only. It is not meant to diagnose or cure a disease.