Pages

Saturday, March 10, 2012

Aryabhata (Who found the number zero - 0)

Aryabhata (IASTĀryabhaṭaSanskritआर्यभट) (476–550 CE) was the first in the line of great mathematician-astronomers from the classical age of Indian mathematics and Indian astronomy. His most famous works are the Āryabhaṭīya (499 CE, when he was 23 years old) and theArya-siddhanta.


Mathematics

Place value system and zero

The place-value system, first seen in the 3rd century Bakhshali Manuscript, was clearly in place in his work. While he did not use a symbol for zero, the French mathematician Georges Ifrah explains that knowledge of zero was implicit in Aryabhata's place-value system as a place holder for the powers of ten with null coefficients
However, Aryabhata did not use the Brahmi numerals. Continuing the Sanskritic tradition from Vedic times, he used letters of the alphabet to denote numbers, expressing quantities, such as the table of sines in a mnemonic form.


Approximation of π

Aryabhata worked on the approximation for pi (\pi), and may have come to the conclusion that \pi is irrational. In the second part of the Aryabhatiyam (gaṇitapāda 10), he writes:
caturadhikam śatamaṣṭaguṇam dvāṣaṣṭistathā sahasrāṇāmayutadvayaviṣkambhasyāsanno vṛttapariṇāhaḥ."Add four to 100, multiply by eight, and then add 62,000. By this rule the circumference of a circle with a diameter of 20,000 can be approached."
This implies that the ratio of the circumference to the diameter is ((4 + 100) × 8 + 62000)/20000 = 62832/20000 = 3.1416, which is accurate to five significant figures.
It is speculated that Aryabhata used the word āsanna (approaching), to mean that not only is this an approximation but that the value is incommensurable (or irrational). If this is correct, it is quite a sophisticated insight, because the irrationality of pi was proved in Europe only in 1761 by Lambert.
After Aryabhatiya was translated into Arabic (c. 820 CE) this approximation was mentioned in Al-Khwarizmi's book on algebra.


Trigonometry

In Ganitapada 6, Aryabhata gives the area of a triangle as
tribhujasya phalashariram samadalakoti bhujardhasamvargah
that translates to: "for a triangle, the result of a perpendicular with the half-side is the area."
Aryabhata discussed the concept of sine in his work by the name of ardha-jya. Literally, it means "half-chord". For simplicity, people started calling it jya. When Arabic writers translated his works from Sanskrit into Arabic, they referred it as jiba. However, in Arabic writings, vowels are omitted, and it was abbreviated as jb. Later writers substituted it with jaib, meaning "pocket" or "fold (in a garment)". (In Arabic, jiba is a meaningless word.) Later in the 12th century, when Gherardo of Cremona translated these writings from Arabic into Latin, he replaced the Arabic jaib with its Latin counterpart, sinus, which means "cove" or "bay". And after that, the sinus became sine in English.


Indeterminate equations

A problem of great interest to Indian mathematicians since ancient times has been to find integer solutions to equations that have the form ax + by = c, a topic that has come to be known as diophantine equations. This is an example from Bhāskara's commentary on Aryabhatiya:
Find the number which gives 5 as the remainder when divided by 8, 4 as the remainder when divided by 9, and 1 as the remainder when divided by 7
That is, find N = 8x+5 = 9y+4 = 7z+1. It turns out that the smallest value for N is 85. In general, diophantine equations, such as this, can be notoriously difficult. They were discussed extensively in ancient Vedic text Sulba Sutras, whose more ancient parts might date to 800 BCE. Aryabhata's method of solving such problems is called the kuṭṭaka (कुट्टक) method.Kuttaka means "pulverizing" or "breaking into small pieces", and the method involves a recursive algorithm for writing the original factors in smaller numbers. Today this algorithm, elaborated by Bhaskara in 621 CE, is the standard method for solving first-order diophantine equations and is often referred to as the Aryabhata algorithm. The diophantine equations are of interest in cryptology, and the RSA Conference, 2006, focused on the kuttaka method and earlier work in the Sulbasutras.


Algebra

In Aryabhatiya Aryabhata provided elegant results for the summation of series of squares and cubes:
1^2 + 2^2 + \cdots + n^2 = {n(n + 1)(2n + 1) \over 6}
and
1^3 + 2^3 + \cdots + n^3 = (1 + 2 + \cdots + n)^2

Tuesday, March 6, 2012

Monday, March 5, 2012

More toxic in the electronic goods

If you want to get rid of electronic equipment that you no longer use and want to protect the environment, follow these steps:

1. Don’t throw old electronics in the trash!
2. Donate for reuse if possible.
3. Find a responsible recycler (an e-Steward) in your state.
4. No e-Steward near you? Try the manufacturers’ free recycling programs
5. Still Can’t Find A Convenient Location? Try other retailers.

Sunday, March 4, 2012

Why sunday is holiday?


Sunday (/ˈsʌnd/ or /ˈsʌndi/) is the day of the week between Saturday and Monday. For most Christians, Sunday is observed as a day for worship of God and rest, due to the belief that it is Lord's Day, the day of Christ's resurrection.
Sunday is a day of rest in most Western countries, part of 'the weekend'. In most Muslim countries, and Israel, Sunday is a working day.
According to the Hebrew calendars, traditional Christian calendars, Sunday is literally the "first day" of the week. According to the International Organization for Standardization ISO 8601 Sunday is the seventh and last day of the week.
No century in the Gregorian calendar starts on a Sunday, whether its first year is '00 or '01. The Jewish New Year never falls on a Sunday. (The rules of the Hebrew calendar are designed such that the first day of Rosh Hashanah will never occur on the first, fourth, or sixth day of the Jewish week; i.e., Sunday, Wednesday, or Friday).

Friday, March 2, 2012

NASA's past mission (1962)


Mariner 1-2 to Venus

Overview:

As plans were getting under way to explore the Moon with the Rangers and Surveyors, JPL and NASA also turned their attention to the rest of the solar system. The Mariner series of missions were designed to be the first U.S. spacecraft to other planets, specifically Venus and Mars. Mariner 1 and 2 were nearly identical spacecraft developed to fly by Venus. The rocket carrying Mariner 1 went off-course during launch on July 22, 1962, and was blown up by a range safety officer about 5 minutes into flight.
A month later, Mariner 2 was launched successfully on August 27, 1962, sending it on a 3-1/2-month flight to Venus. On the way it measured for the first time the solar wind, a constant stream of charged particles flowing outward from the Sun. It also measured interplanetary dust, which turned out to be more scarce than predicted. In addition, Mariner 2 detected high-energy charged particles coming from the Sun, including several brief solar flares, as well as cosmic rays from outside the solar system.
As it flew by Venus on December 14, 1962, Mariner 2 scanned the planet with infrared and microwave radiometers, revealing that Venus has cool clouds and an extremely hot surface. (Because the bright, opaque clouds hide the planet's surface, Mariner 2 was not outfitted with a camera.)
Mariner 2's signal was tracked until January 3, 1963. The spacecraft remains in orbit around the Sun.

Mission Details:

Mass: 203 kilograms (447 pounds)
Science instruments: Microwave radiometer, infrared radiometer, flux-gate magnetometer, ion chamber and Geiger-Mueller counters, cosmic dust detector, solar plasma detector

Fast facts:

Mariner 1 launch: July 22, 1962
Mariner 2: August 27, 1962
Mariner 2 Venus flyby: December 14, 1962

articles from NASA - http://www.nasa.gov/

Facts about Planets


  • Mercury is the second smallest planet in the solar system and has no moon. It can get as hot as 800º C and cold as 300º C below zero. One year on Mercury is equal to 88 days on Earth. It is named after the Roman God of Commerce.
  • Venus is the only planet that rotates from east to west. A year on this planet is equal to 225 days on Earth.
  • Earth is nearly 93 million miles away from the Sun. It takes about 16 million horsepower to break the Earth's gravitational pull.
  • According to scientists, in around 5 billion years, a day on Earth will be 48 hours long and somewhere during that time the Sun will explode.
  • The planet Neptune was discovered more than150 years ago in 1846, and since then it still has to complete an orbit around the Sun, as one Neptune year equals to 165 Earth years.
  • Pluto does not have a fixed orbit and its orbit comes in the middle of Neptune's orbit. Also, Pluto's size is very small which made scientists demote it to a dwarf planet status.

Recycling everybody know

You can get gold form computer components and old mobile phones.
Recycling is processing used materials (waste) into new products to prevent waste of potentially useful materials, reduce the consumption of fresh raw materials, reduce energy usage, reduce air pollution (from incineration) and water pollution (from landfilling) by reducing the need for "conventional" waste disposal, and lower greenhouse gas emissions as compared to virgin production. Recycling is a key component of modern waste reduction and is the third component of the "Reduce, Reuse, Recycle" waste hierarchy.
There are some ISO standards relating to recycling such as ISO 15270:2008 for plastics waste and ISO 14001:2004 for environmental management control of recycling practice.
Recyclable materials include many kinds of glass, paper, metal, plastic, textiles, and electronics. Although similar in effect, the composting or other reuse of biodegradable waste – such as food or garden waste – is not typically considered recycling. Materials to be recycled are either brought to a collection center or picked up from the curbside, then sorted, cleaned, and reprocessed into new materials bound for manufacturing.
In the strictest sense, recycling of a material would produce a fresh supply of the same material—for example, used office paper would be converted into new office paper, or used foamed polystyrene into new polystyrene. However, this is often difficult or too expensive (compared with producing the same product from raw materials or other sources), so "recycling" of many products or materials involves their reuse in producing different materials (e.g., paperboard) instead. Another form of recycling is the salvage of certain materials from complex products, either due to their intrinsic value (e.g., lead from car batteries, or gold from computer components), or due to their hazardous nature (e.g., removal and reuse of mercury from various items). Critics dispute the net economic and environmental benefits of recycling over its costs, and suggest that proponents of recycling often make matters worse and suffer from confirmation bias. Specifically, critics argue that the costs and energy used in collection and transportation detract from (and outweigh) the costs and energy saved in the production process; also that the jobs produced by the recycling industry can be a poor trade for the jobs lost in logging, mining, and other industries associated with virgin production; and that materials such as paper pulp can only be recycled a few times before material degradation prevents further recycling. Proponents of recycling dispute each of these claims, and the validity of arguments from both sides has led to enduring controversy.

your Toothpaste Tube


Looking for a refreshing alternative to throwing away your toothpaste tubes? This easy do-it-yourself project up cycles your empty tubes into a simple toothbrush holder. Up cycling materials like these are a great way to reuse without costing a mint.

Materials:
  • 5 empty toothpaste tubes
  • scissors
  • ruler
  • clear tape
  • hole punch
  • ribbon or plastic lanyard
  • binder clips

Instructions:

1. Collect five Colgate® toothpaste tubes. Clean them by cutting off the bottom and slipping your scissors into the side seam. Flatten them out and clean with soap and water.

2. Cut four tubes to 3 ½” x 4 ½” and one tube into a 3 ½” x 3 ½” square. Fold down the top ½” of the four rectangular tubes and tape.

3. Take one of the four rectangles and punch holes every ½” along the two tall sides and along the short bottom side that is not folded. Use this punched piece as a template and punch holes in the exact same spots on the other three rectangular pieces.

4. To punch the small square piece, line up the short punched side of the rectangle piece with any side of the short piece. Repeat punching holes for the other three sides of the square using the short side of the rectangular piece as a template.

5. Then punch two holes near the center of the square. This will be the bottom of the container and the holes will be for drainage.

6. Match up two large pieces and lace up one side tying it off at the top and bottom. Open it up. On one of the non-laced ends, attach to the next rectangular piece in the same way with the printed sides facing out. Repeat for each additional rectangular piece. When you’ve laced all four pieces, connect the two end pieces together and lace creating a cube with your pieces.

7. Match up the square piece with the bottom of the container. Use binder clips to hold it in place. Lace around the bottom of the container and tie it off. You’re ready to put your upcycled toothbrush holder into action. 

Thursday, March 1, 2012

Facts about the sun


  1. The Sun is 4.5 billion years old and produces 383 billion trillion kilowatts of energy.
  2. Sunlight takes 8 minutes to reach the Earth and is responsible for the ocean currents and weather patterns on our planet.
  3. The Earth orbits the Sun in an elliptical uneven orbit and the distance between them varies depending on where the Earth lies in that orbit.
  4. The Sun is only an average size for a star but still accounts for 98% of the total matter in our solar system.
  5. The solar winds produced by the Sun extends to about 50AU, where AU is the distance from the Earth to the Sun.
  6. The lightning in the sky is nearly 3 times hotter than the Sun.

Interesting Facts About Your Body


  1. It takes your food seven seconds to get from your mouth to your stomach.
  2. One human hair can support 3 kg (6.6 lb).
  3. Human thighbones are stronger than concrete.
  4. A woman's heart beats faster than a man's.
  5. There are about one trillion bacteria on each of your feet.
  6. Women blink twice as often as men.
  7. The average person's skin weighs twice as much as the brain.
  8. Your body uses 300 muscles to balance itself when you are standing still.
  9. If saliva cannot dissolve something, you cannot taste it.
  10. One out of every 2,000 newborn infants has a tooth when they are born.
  11. After the first trimester, a fetus has fingerprints. They will be unique only to him or her for their entire life.
  12. Fingernails and toenails can grow from the base to the point within 6 months. Some people’s nails grow faster than others.
  13. Toenails grow slower than fingernails.
  14. A sneeze travels at a rate in excess of 100 miles per hour.
  15. If a person goes without sleep for 10 days, they will die. They will die sooner from lack of sleep than they will from starvation.
  16. A blood cell can make a complete circuit of the human body in about 60 seconds.
  17. There are 20 feet of blood vessels in each square inch of human skin.
  18. Each human spends a half hour as a single cell when it is first conceived.
  19. Your body has enough iron in it to make a nail 3 inches long.