the-french-artist/wikipedia_20220301.simple_sentence_split huggingface dataset:
But farms are much larger than gardens.
A farm may have hundreds of square kilometers of plants and crops.
A garden in a person's backyard is usually only measures a few square meters.
Farms are businesses which sell the crops, fruit, and vegetables that are produced.
Some gardens are businesses, which charge a fee to enter the garden.
However, private gardens in people's backyards are used as a hobby or as a recreation, not as a business.
Features of gardens
In addition to plants, many gardens also have landscaping features such as pathways, seats, rock gardens, ponds, fountains, a small stream with or without a waterfall.
Some incorporate gazebos and structural designs to accommodate for places to sit or to place a hammock for a siesta.
Roman gardens will have its own columns, fountains and statures placed at strategic places depending on its sizes and uses.
Japanese gardens have their own unique designs and features.
Role of gardens
Some gardens are created in people's backyards, outside their home (note that in Britain the whole area is called a "garden", not a "yard").
People with gardens in their backyards use gardens as a place to do gardening.
Gardening is a type of physical activity which can use enough energy and increase your heart rate that it can be rated as a form of exercise for to relax and exercise certain muscles depending on whether on the activity you do that day such as planting, pruning, weeding, or simply just walk around your garden continuously for 15 minutes or more.
Many people find gardens relaxing especially if the garden is full flowers with strong scents.
Some flowers like roses, bougainvilleas, orchids and many others are just beautiful to look at.
Many people think that gardens are very beautiful and a place to relax and /or entertain.
A garden can have a place to barbecue, to sit and to read.
In many countries and cultures, designing pretty gardens is considered to be an art.
In Japan, for instance, Zen monks build decorative gardens with stone and waterfall features using natural materials such as bamboo, rock and BONSAI trees like spruce, pine, and other trees with they trained into miniature forms.
In Europe in the 1700s, kings and queens had formal gardens built (for example, the gardens at Versailles, France).
In China they also feature Chinese forms of gardens.
Now some enterprising people start to have herbal gardens to feature useful herbs used in alternative, traditional, and homeopathic medicine
Great Zimbabwe is a ruined city in the south-eastern hills of Zimbabwe.
The site is not far from the country's border with Mozambique, which is in the southeast of the African continent.
Greater Zimbabwe was the capital of the Kingdom of Zimbabwe during the country’s later Iron Age.
The monument first began to be built in the 11th century, and work continued until the 14th century.
It covered an area of  722 hectares (1,780 acres) which might have housed up to 18,000 people.
It was a royal city for the Zimbabwean monarch.
One of its most prominent features were its walls, some of which were over five metres high and which were constructed without mortar.
Eventually the city was abandoned and fell into ruin.
The Kingdom of Zimbabwe included the River Zambezi in the north, the Transvaal in the south and Botswana in the east.
The people who lived at Great Zimbabwe controlled trade between the coast and inland Africa.
The modern country of Zimbabwe is named after it.
Archaeologists have found goods from as far as China that were used by the people.
This shows they bought and sold things over great distances.
The city had stopped growing when traders from Portugal came to southern Africa 500 years ago, but nobody is sure why this happened.
Europeans at first thought that Great Zimbabwe had been built by foreigners.
Now we know it was built by the local people.
People who have studied the site have learned much about old Africa.
The earliest known written mention of the ruins was in 1531 by Vicente Pegado, Captain of the Portuguese garrison of Sofala, who recorded it as Symbaoe.
The first visits by Europeans were in the late 19th century, with investigations of the site starting in 1871.
History of Zimbabwe
Cities in Zimbabwe
World Heritage Sites in Africa
Prehistoric Africa
11th-century establishments in Africa
15th-century disestablishments
Machu Picchu is a pre-Columbian 15th-century Inca site in Peru, in South America.
The Incas built the city on a mountain ridge, 2430m above sea level.
They lived there between 1200 and 1450 AD.
Other people lived there before about 650 AD.
The Incas built houses, fields and temples by cutting the rock on the mountain so it was flat.
They built an observatory to look at the stars.
When the Spanish invaded Peru, the Incas left Machu Picchu.
Nobody knows for sure why they did that, but some think it was because of diseases from Europe.
The city was left unfinished, most likely due to the Spanish invasion and/or a civil war between the ruling rival Inca brothers named Huascar and Atahualpa.
The Spanish never found Machu Picchu or the lost city during their occupation.
Machu Picchu is very difficult to get to because it is so high in the mountains.
It has only one way in and a stone wall to protect it.
Most people on Earth did not know it was there until a Yale graduate named Hiram Bingham rediscovered it in 1911.
He heard rumours of a hidden city which was already known to the native Peruvians, who guided him there.
He led a restoration project that was partly funded by the National Geographic Society.
Bingham made a deal with the government to take artifacts to the Peabody Museum for study.
Peru is still trying to have those artifacts returned to them.
Machu Picchu was declared a Peruvian Historical Sanctuary in 1981 and a UNESCO World Heritage Site in 1983.
In 2007, Machu Picchu was voted one of the New Seven Wonders of the World in a worldwide Internet poll.
Today, there is a new road so that tourists can visit.
People can also walk along the Inca Trail, or take a train from Cusco.
Information About Machu Picchu
QuickTime Virtual Tour of Machu Picchu and Peru from destination360.com.
Machu Picchu on National Geographic
Machu Picchu on Google Maps.
Machu Picchu travel guide.
Machu Picchu.
World Heritage Sites in South America
1450s establishments
Establishments in Peru
1572 disestablishments
16th-century disestablishments in South America
a written medium, for instance:
an academic journal
a diary
a literary magazine, a periodical devoted to literature
a daily newspaper
a scientific journal
Journal (mechanical device), the section of a rotating shaft that contacts and turns in a plain bearing
Mining journal, a record systematically describing the strata through which a mine shaft passes (see shaft mining)
Journal entry, an accounting transaction in the double-entry bookkeeping system
Apple Inc. is a multinational company that makes personal computers (the Macintoshes), mobile devices (iPod, iPhone and iPad), and software (macOS, iOS, watchOS and tvOS).
Apple calls its computers Macintoshes or Macs, and it calls its laptops MacBooks.
Their line of mobile music players is called iPod, their smartphone line is called iPhone and their tablet line is called iPad.
Apple sells their products all around the world.
Apple Inc. used to be called Apple Computer, Inc., but Apple changed their name after introducing the original iPhone.
Apple Inc. is a public company and trades on the NASDAQ under the stock ticker AAPL.
On March 19, 2015, it became one of the 30 components of the Dow Jones Industrial Average.
General history
Apple was started in 1976 by Steve Jobs and Steve Wozniak.
Before they made the company, they sold "blue boxes", which had telephone buttons on them.
People could use them to make telephone calls from payphones without paying any money.
It did this by pretending to be a telephone operator.
The company's first product is now called the Apple I computer.
They were almost ready to sell it, but a problem happened.
Steve Wozniak was working for the computer company Hewlett-Packard, and the papers that said he could work there said he had to give everything he invented to the company before he could do what he wanted to do with it.
He showed the first Apple I to the boss at Hewlett-Packard, but they did not want his computer.
Wozniak was then free to do what he wanted to do with the Apple I. It began selling in 1976.
In 1977, they made their second computer, called the Apple II, which later became very successful compared to Apple I.
Before the iPhone, the most popular product made by Apple was the iPod.
It was first sold in 2001, and Apple sold over 100 million in six years.
iPods are used to play music.
Recent iPod Touches have a LED screens, can take and show pictures, record, view and edit videos, record word and voice memos, can connect to the Internet for features such as e-mail, and downloading apps from the App Store.
The latest iPod Touch is made with a 64-bit architecture.
iPod shuffle (4th generation)
iPod shuffle 2 GB - This model has no screen.
Instead, it has a click wheel to control the music, and is very small.
It was the cheapest iPod at the time.
People can sync playlists and Genius mixes but apart from that, it has only basic music playback functions, and also has feature called VoiceOver.
It comes in five different colors: silver, orange, pink, green, and blue.
A polished stainless steel version is available.
It can store about 1,000 songs.
iPod nano 8 GB - The 8GB could store about 2,000 songs.
It was discontinued.
iPod nano 16 GB - Comes in space gray, purple, blue, silver, green, yellow, and pink.
It can hold about 4,000 songs.
iPod classic 160 GB - comes in black or silver.
This is the chunkiest and most original looking iPod, but the best music holder.
It can hold about 40,000 songs.
iPod touch 8 GB - Apple announced the fifth generation iPod Touch in 2012, equipping it with a front and rear facing camera, a better display, a better processor for faster performance, and it has a thin new design.
It can also run the latest operating system, iOS 9.
This makes it a lot closer to the iPhone 5.
The 8GB model is discontinued.
iPod touch 16 GB - has a multi-touch screen and looks much like the iPhone.
It can be used to view high quality media and to use the Internet, using built-in Wi-fi.
Some say it is like an iPhone without the phone.
This model can hold about 4,000 songs, but was discontinued in September 2009, and was now put up again to replace the 8 GB in June 2013.
iPod touch 32 GB - This model can hold about 7,000 songs.
It first went on sale in February 2008.
iPod touch 64 GB - This model can hold about 14,000 songs.
It first went on sale in September 2009.
(PRODUCT) RED
The red iPod shuffle, iPod nano, and iPod touch models, and a few more products, are part of the "(PRODUCT) RED" program.
This means that some of the profits from these iPods goes to the Global Fund to fight AIDS in Africa.
Apple makes computers.
Newer computers by Apple run the OS X operating system, which is included with the Mac.
MacBook (very skinny and light laptop designed for average users, discontinued)
MacBook Pro (more powerful and fast laptop designed for professional users)
MacBook Air (skinny and light laptop, less expensive than MacBook , but does not include a Retina display option which the Macbook did.
After the Macbook was discontinued the Air got the Retina display)
Mac Mini (a very tiny, but fully functional computer that does not come with its own monitor, keyboard, or mouse.
Used mainly for home and school)
iMac (a computer where everything is built in behind the screen, designed for many uses, such as home, school, and professional (i.e.: Photoshop) use)
Mac Pro (a very powerful, fast computer that does not come with its own monitor, for professional people who need fast computers, i.e.: movie editing)
Apple also makes software for their computers.
Some of the software that Apple makes is:
iLife (a set of programs designed for everyday use) contains iMovie, a program for making movies, GarageBand, a program for making music, iPhoto, a program for organizing photos, iTunes, a program for organizing (and buying) music, iWeb (not sold or updated any more), a program for making web pages, and iDVD (also no longer sold or updated), a program to make DVDs.
These programs are considered very simple to use.
iWork (a set of programs for office work) contains Pages, a program for making documents and Keynote, a program for making slideshows, and "Numbers" for making spreadsheets.
These apps are available on Apple Mac computers, iPhones, iPads and iPod Touchs.
Professional program to make movies called Final Cut Pro, a program for music making called Soundtrack Pro, Motion, a program for high-quality moving graphics authorship, and DVD Studio Pro, a program used to make professional DVDs.
Final Cut Express (a set of programs similar to Final Cut Pro, but simplified and cheaper)
Aperture (for professional photographers to edit their photos, no longer supported or updated)
Logic Studio (A set of programs where professionals can edit and produce audio)
Logic Express (a set of programs similar to Logic Studio, but simplified and cheaper)
Most computer users in the world use Microsoft Windows, the rival to Mac OS X. About 10% of computer users use Apple's Macintosh computers.
It is not legal to run Apple's Mac OS X on a Windows computer.
However, it is allowed to run Windows on modern Macintosh computers.
Even though Apple makes their computers to run Mac OS X, they also make software that allows you to install Windows.
This software is called Boot Camp.
Apple is perhaps most famous for its mobile devices, which are small computers that are easy to carry around.
They have touchscreens with multi-touch technology instead of a separate keyboard and mouse.
Most of these products run an operating system called iOS.
It is very similar to the Android software made by Google.
iOS can do a lot of different things, and it does so by running "apps", which are programs similar to those on a PC.
Users can download and buy more apps for their device from Apple's App Store.
The iPhone is a mobile phone that can be used to make calls, send text messages, play games and music, show photos and videos (like an iPod), browse the Internet, and do much more.
It was one of the first smartphones in the world when the first version was announced in 2007.
Apple makes and sells a different model every year, with new models being faster and more powerful and having a newer version of iOS than those that come before them.
The newest iPhones released are the iPhone 12 and the iPhone 12 Pro which run on iOS 14.
Many cellular carriers around the world sell iPhones, including Sprint, Verizon, AT&T, and T-Mobile in the US.
The iPad is a tablet computer, similar to the iPhone and iPod Touch but with a much larger display - while a typical iPhone has a screen about 4 to 5 inches in size, iPads have screens from 8 to 12 inches big.
The first iPad was introduced in 2010 and along with the iPhone, new and better models are made and sold every year.
A new iPad will ship with the latest iPad OS software if it is supported.
The Apple Watch is an example of "wearable technology", because it is worn around the wrist in the same way as a traditional wristwatch.
However, it is much more than a wristwatch.
It not only tells the time and date but also tracks the fitness of the person wearing it and monitors the person's health.
It can also do many of the same things that an iPhone can do, such as use Apple's Siri personal assistant, but it needs to be "paired" with an iPhone for it to do these things, meaning that it will not work if you do not have an iPhone.
The Apple Watch has many different designs: there is the standard version, a "Sport" version designed for athletes, and an "Edition" version which is made as a fashion product.
These all run "watchOS", a modified version of iOS.
The Apple TV is a box that plugs into a TV.
It can connect wirelessly to any computer that has the Apple program iTunes on it.
The Apple TV can play music and show photos or videos from iTunes on the TV.
Like other Apple products, Apple TV is regularly updated with new software and features.
The most recent version comes with a new remote control and includes the Siri voice assistant.
It uses tvOS, a TV version of iOS.
Following several campaigns (for example, Green my Apple), Apple has made their products better for the environment.
Previously, the notebook line removed many toxins and improved the products battery life and recharge cycles.
Apple products used to ship with chargers and EarPods, but recently Apple has removed the chargers and EarPods from the boxes of most of their products to make the cases smaller.
Apple says they did this to make it easier to make and save resources and energy.
The MacBook uses a power efficient CPU, M1, and has a power-efficient Retina display, and is slimmer than previous models.
The MacBook, MacBook Pro, and MacBook Air have highly recyclable aluminium and glass enclosures, mercury-free displays and arsenic-free display glass.
The printed circuit boards, electrical components, mechanical parts, and internal cables are BFR-free and PVC-free.
The MacBook, MacBook Air, MacBook Pro, and the LED Cinema Display contain energy-efficient LED display technology.
The MacBook LED-backlit display uses 30% less power compared to conventional CCFL-backlit displays.
Sleep-mode energy usage has decreased 93% between the first-generation and current-generation iMac.
This is due to improvements in CPU power management and increased hardware efficiency.
Between the fourth-generation iPod nano and the first-generation iPod nano, the packaging is 32% lighter and uses 54% less volume.
Apple products are compliant with the European Directive on the Restriction of the Use of Certain Hazardous Substances in Electrical and Electronic Equipment, also known as the RoHS directive.
Examples of materials restricted by RoHS include lead, mercury, cadmium, hexavalent chromium, and PBB and PBDE flame retardants.
Apple met many of the RoHS requirements long before the July 2006 deadline.
Starting from the iPhone 12, iPhone 12 Pro and Apple Watch Series 6, Apple products stopped shipping with chargers and EarPods as an incentive for users to reuse previous accessories.
CEOs
1977–1981: Michael Scott
1981–1983: Mike Markkula
1983–1993: John Sculley
1993–1996: Michael Spindler
1996–1997: Gil Amelio
1997–2011: Steve Jobs (Interim CEO 1997–2000)
2004, 2009, 2011–present: Tim Cook (Acting CEO during Steve Jobs' health issues; replaced Steve Jobs after he resigned)
Directors
Arthur D. Levinson, Chairman and CEO of Genentech
James A. Bell, retired President of Boeing
Al Gore, Former Vice President of the United States
Andrea Jung, Chairman and CEO of Avon Products
Ronald Sugar, former chairman and CEO of Northrop Grumman
Susan Wagner, co-founder of BlackRock
Arthur D. Levinson, Chairman
Tim Cook, CEO
Jeff Williams, COO
Since the formation of the Apple Computer Company in 1977, Apple has employed over 95,000 people worldwide.
The majority of Apple's employees have been in the United States but Apple has substantial manufacturing, sales, marketing, and support organizations worldwide, with some engineering operations in Paris and Tokyo.
Apple Corps has sued Apple Inc. many times for trademark infringement.
In the first case, Apple Inc. agreed not to go into the music industry.
Apple Corps believes this agreement was broken when Apple Inc. launched the iTunes Store, Apple's online music store.
The two companies had trouble in the past, over the use of the Apple name.
They made a deal that Apple Computers would not act as a music company.
When Apple Computer Inc. began to sell their iPod, and set up their iTunes music store, Apple Corps believed they had broken their agreement, and took them to court.
Apple Computers won the case, but the two companies later worked out a new deal.
This deal now means that the Beatles music is now on the iTunes store, whereas it was not there before.
Apple Computers was then renamed as Apple Inc. because of its mobile technology business.
Steve Jobs, then CEO of Apple, Inc., has said in the past that he loves music from The Beatles, which can be considered to be very ironic.
Pixar, an animation studio founded by Steve Jobs, one of the founders of Apple.
1976 establishments in California
Soil is loose material which lies on top of the land.
It has many things in it, like tiny grains of rock, minerals, water and air.
Soil also has living things and dead things in it: "organic matter".
Soil is important for life on Earth.
Because soil holds water and nutrients, it is an ideal place for plants to grow.
Soil holds the roots, and lets plants stand above the ground to collect the light they need to live.
Almost as important are the fungi.
There are fungi which grow into plant roots, a symbiosis known as mycorrhiza.
This helps trees grow.
There are many other fungi that live by breaking down dead organic material: the remains of other living things.
The broken down material is a main source of plant nutrients.
Many animals dig into the soil and make the soil their home.
The large animals use soil to make dens for sleeping and giving birth.
The small animals live most of their life in the soil.
Earthworms are famous for improving soil.
This is because the holes they make let air go into the soil.
The holes also let water go through.
The soil also has many microorganisms living in it.
Many of them eat the organic material in the soil.
They use oxygen and release carbon dioxide.
They also release mineral nutrients into the soil.
Soil is different in different places on Earth.
This is because the climate and rocks in the Earth are different in different places on Earth.
Soils are usually thicker in places where ice sheets covered the ground during the Pleistocene ice ages.
This is because the ice sheets ground the rock into powder as they slowly moved over the surface.
What soil is made of
It has rock pieces and the rocks are made of minerals,
It has dead and living things (organic matter, humus),
It has water.
It has air.
Soil has rock pieces made small by wind and rain and sun and snow.
The rocks are made of minerals and some of the minerals dissolve in water.
Some of the minerals dissolved in water can be used as food by plants.
Soil also has dead and living things (organic matter) in it.
When a plant dies, it is eaten by animals including bacteria in the soil.
When the bacteria are done eating, what is left behind is called humus.
When the bacteria die the plant food (minerals) goes back into the soil.
A food for plants is called a "plant nutrient".
There are many kinds of plant nutrients.
Soil has many empty spaces.
Half of the soil is space.
The spaces are filled with water and air.
Water can enter the spaces in the soil.
Plants drink the water and the minerals in the water.
Plant roots need air to live.
If plant roots do not have air, the roots will die.
If the plant roots die, the plant will die.
A plant that dies is eaten by bacteria and becomes plant nutrients again.
There are many kinds of soil.
Each kind of soil has big and small rocks in it and some humus.
If rocks in a soil are as big as your fingers, we call those rocks "gravel".
Smaller rocks are called sand.
Very small rocks are called silt.
Very, very small rocks are called clay.
You can see sand with your eye.
Sand feels rough between your toes.
Silt rock is very small and you must use a lens to see silt.
Silt rock is smooth between your toes.
Clay rock is too small to see with a lens.
To see the smallest things you must use a big microscope.
You must use a big microscope to see clay too.
Clay rock feels slippery between your toes.
Most soils contain all kinds of small rocks.
The three best rocks for making soil are sand, silt, and clay.
Soil texture
Every soil has different amounts of sand and silt and clay.
The mix of sand and silt and clay is the "texture" of the soil.
We can also say the mix has a "soil texture".
A soil with a lot of sand is called a "sandy soil texture".
A soil with a lot of silt is called a "silt soil texture".
A soil with a lot of clay is called a "clay soil texture".
Farmers like to grow food in the best soil.
The best soil is half sand and some silt and a little clay.
The organic matter found in the soil is not counted in the soil texture.
Only the rocks are counted when we discover the soil texture.
Soil texture is very important.
Clay and humus are special parts of the soil.
They help keep water and plant food (plant nutrients) in the soil.
Water and plant nutrients stick to clay and humus.
Water sticks to all of the rock in the soil.
But, water sticks best to clay.
Water is taken into (absorbed) into humus like a sponge absorbs water.
Humus holds a lot of water and plant nutrients.
Clay and humus keep water and plant nutrients in the soil.
Sand will hold only a little water in the soil.
If the soil has too much sand, the water will flow down into the earth.
The water that flows down takes plant nutrients down too.
The plant roots can not get at the water and plant nutrients if they go too deep.
It is best for soil to have a little bit of clay and humus in it for growing plants.
Soil structure (clumps)
The smallest parts of soil are sand and silt and clay.
Those small parts join to make larger parts we call "clumps" or "aggregates".
The clumps are made when sand and silt and clay stick together.
The humus and clay and  minerals in the soil are like glue.
The glue sticks the sand and silt and clay together and makes clumps.
The clumps make shapes by themselves.
Some soils have small round clumps.
Other soils have large, hard and flat clumps.
The soil with small round clumps is best because it lets in air and water.
A little glue is best.
If the soil has only a little glue there will be space for water and air and the soil will be soft.
If the soil has too much glue the soil will be hard.
If the soil has no glue, there will be no space in the soil for air and water.
A soil with no spaces is not healthy.
Worms in the soil make a slippery glue.
When worms make holes in the soil they leave some glue in the soil.
Plant roots also make spaces in the soil.
When the roots die they leave holes in the soil.
Soil horizons (layers)
A soil has a "soil texture" (sand and silt and clay) and it has organic matter mixed in it.
But weather changes the soil.
It is cold on the Earth near the north and south poles.
It is hot near the equator of the Earth.
Some places on Earth get a lot of rain and some places get no rain.
Hot and wet weather make one kind of soil.
Cold and dry weather make another kind of soil.
Rain water makes small things in the soil move down with the water.
When the things in the water get stuck in the soil those things make a layer in the soil.
If you dig down into the soil you may find many layers in the soil.
The layers may have different colors.
The layers may have different "soil textures".
The top part of the soil may have a lot of humus and sand.
Below that layer there may be a layer of silt.
Below that layer there may be a layer of clay.
The sand stays on the top because it is large.
The silt goes down a little with the water and makes a layer because it is small.
The silt is smaller than some of the spaces in the soil.
The clay can go down even lower with the water because it is the smallest.
The sand will make one layer, the silt will make another layer and the clay will make another layer.
The humus can move down with the water and make a layer too.
The silt and clay and humus can move down because of the spaces in the soil.
But, the silt, clay, and humus will fill the spaces in the soil.
When the spaces in the soil are closed, it makes it hard for air to go into the soil.
Plant roots do not go where there is no air.
When we dig down we find layers in the soil.
We call those layers "soil horizons".
The top horizon may be an inch (25mm) thick.
We call that layer the "O" horizon or sometimes "topsoil".
The next layer (horizon) is the "B" horizon.
The next lower layer of soil is the "C" horizon.
The bottom layer has many rocks and may be called the bedrock or "R" horizon for "rock".
Deep down, there is always bedrock.
But you may have to dig down a mile (a km) or more.
When the soil dries, the soil may shrink and cracks will form in the soil.
The soil in the top layer may fall down into the cracks.
This causes the layers of soil to be changed because they are mixed.
There may be many types soil where you live or only one type of soil.
Different rocks make different soil textures.
Different weather makes the different soil textures different.
And so, there are different soils all over the world.
Soil fertility
short video about soil from The Guardian newspaper
Something of, or relating to, an organism
Organic chemistry, chemistry that is based on carbon, which is the basis for all living things.
Organic matter in soil is material that is, or once was, a plant or animal.
Organic farming, agriculture conducted according to certain standards, especially the use of only naturally produced fertilizers and non-chemical means of pest control.
3D (or 3-D) means three-dimensional, or having three dimensions.
For example, a box is three-dimensional; it is solid, and not thin like a piece of paper.
It has volume, a top and bottom, left and right (sides), as well as a front and back.
You can turn the box around to view it from another side (called a face, surface or simply side).
The three dimensions are often called length (or depth), width (or breadth), and height.
Some purposes use other words.
3D graphics are used to make video games or animated movies.
Many calculations are needed to make pictures seem three-dimensional on a screen.
Modern computers usually have a GPU (Graphics Processing Unit) to handle these calculations.
In mathematics
In the Cartesian coordinate system, length, width, and height are given in letters (variables) to make them easier to write, or if a value is not known.
Often X is width, Y is height, and Z is length.
Other 3D coordinate systems such as spherical coordinates include both linear and angular measurements.
Some people see time as a fourth dimension.
It is also measured.
It is measured in units of time such as seconds, hours, years, or any other measurement of time.
Humidity means water vapor in the air, but not to liquid droplets in fog, clouds, or rain.
Deserts usually have low humidity, and tropical regions have high humidity.
The word "humid" often means that the humidity is high, which gives the feeling of being very damp (wet air), stuffy, or even sweltering when the temperature is also high.
When the humidity is low, the air can be said to be "not humid" or "dry."
The term "relative humidity" is used to note the amount of humidity as a percent, from 0-100%.
Meteorologists use  hygrometers to measure the humidity in the air.
Humidity affects the rate of evaporation.
With a higher humidity, the rate of evaporation is less.
A Calabi–Yau manifold, or 'Calabi–Yau space', is a special type of manifold.
It is described in certain branches of mathematics such as algebraic geometry.
The Calabi–Yau manifold's properties, such as Ricci flatness, have applications in theoretical physics.
Particularly in superstring theory, the extra dimensions of spacetime might take the form of a 6-dimensional Calabi–Yau manifold.
This led to the idea of  string theory mirror symmetry.
Quantum mechanics explain how the universe works at a scale smaller than atoms.
It is also called quantum physics or quantum theory.
Mechanics is the part of physics that explains how things move and quantum is the Latin word for 'how much'.
A quantum of energy is the least amount possible (or the least extra amount), and quantum mechanics describes how that energy moves or interacts.
Atoms used to be considered the smallest building blocks of matter, but modern science has shown that there are even smaller particles, like protons, neutrons and electrons.
Quantum mechanics describes how the particles that make up atoms work.
Quantum mechanics also tells us how electromagnetic waves (like light) work.
Wave–particle duality means that particles behave like waves and waves behave like particles. (
They are not two kinds of thing, they are something like both: this is their duality.)
Much of modern physics and chemistry can be described and understood using the mathematical rules of quantum mechanics.
Waves and photons
Photons are particles that are point-sized, tinier than atoms.
Photons are like "packets" or packages of energy.
Light sources such as candles or lasers produce light in bits called photons.
The more photons a lamp produces, the brighter the light.
Light is a form of energy that behaves like the waves in water or radio waves.
The distance between the top of one wave and the top of the next wave is called a 'wavelength'.
Each photon carries a certain amount, or 'quantum', of energy depending on its wavelength.
A light's color depends on its wavelength.
The color violet (the bottom or innermost color of the rainbow) has a wavelength of about 400 nm ("nanometers") which is 0.00004 centimeters or 0.000016 inches.
Photons with wavelengths of 10-400 nm are called ultraviolet (or UV) light.
Such light cannot be seen by the human eye.
On the other end of the spectrum, red light is about 700 nm.
Infrared light is about 700 nm to 300,000 nm.
Human eyes are not sensitive to infrared light either.
Wavelengths are not always so small.
Radio waves have longer wavelengths.
The wavelengths for an FM radio can be several meters in length (for example, stations transmitting on 99.5 FM are emitting radio energy with a wavelength of about 3 meters, which is about 10 feet).
Each photon has a certain amount of energy related to its wavelength.
The shorter the wavelength of a photon, the greater its energy.
For example, an ultraviolet photon has more energy than an infrared photon.
Wavelength and frequency (the number of times the wave crests per second) are inversely proportional, which means a longer wavelength will have a lower frequency, and vice versa.
If the color of the light is infrared (lower in frequency than red light), each photon can heat up what it hits.
So, if a strong infrared lamp (a heat lamp) is pointed at a person, that person will feel warm, or even hot, because of the energy stored in the many photons.
The surface of the infrared lamp may even get hot enough to burn someone who may touch it.
Humans cannot see infrared light, but we can feel the radiation in the form of heat.
For example, a person walking by a brick building that has been heated by the sun will feel heat from the building without having to touch it.
The mathematical equations of quantum mechanics are abstract, which means it is impossible to know the exact physical properties of a particle (like its position or momentum) for sure.
Instead, a mathematical function called the wavefunction provides information about the probability with which a particle has a given property.
For example, the wavefunction can tell you what the probability is that a particle can be found in a certain location, but it can't tell you where it is for sure.
Because of this uncertainty and other factors, you cannot use classical mechanics (the physics that describe how large objects move) to predict the motion of quantum particles.
Ultraviolet light is higher in frequency than violet light, such that it is not even in the visible light range.
Each photon in the ultraviolet range has a lot of energy, enough to hurt skin cells and cause a sunburn.
In fact, most forms of sunburn are not caused by heat; they are caused by the high energy of the sun's UV rays damaging your skin cells.
Even higher frequencies of light (or electromagnetic radiation) can penetrate deeper into the body and cause even more damage.
X-rays have so much energy that they can go deep into the human body and kill cells.
Humans cannot see or feel ultraviolet light or x-rays.
They may only know they have been under such high frequency light when they get a radiation burn.
Areas where it is important to kill germs often use ultraviolet lamps to destroy bacteria, fungi, etc.
X-rays are sometimes used to kill cancer cells.
Quantum mechanics started when it was discovered that if a particle has a certain frequency, it must also have a certain amount of energy.
Energy is proportional to frequency (E ∝ f).
The higher the frequency, the more energy a photon has, and the more damage it can do.
Quantum mechanics later grew to explain the internal structure of atoms.
Quantum mechanics also explains the way that a photon can interfere with itself, and many other things never imagined in classical physics.
Max Planck discovered the relationship between frequency and energy.
Nobody before had ever guessed that frequency is directly proportional to energy (this means that as one of them doubles, the other does, too).
Under what are called natural units, then the number representing the frequency of a photon would also represent its energy.
The equation would then be:
But the way physics grew, there was no natural connection between the units that were used to measure energy and the units commonly used to measure time (and therefore frequency).
So the formula that Planck worked out to make the numbers all come out right was:
or, energy equals h times frequency.
This h is a number called Planck's constant after its discoverer.
Quantum mechanics is based on the knowledge that a photon of a certain frequency means a photon of a certain amount of energy.
Besides that relationship, a specific kind of atom can only give off certain frequencies of radiation, so it can also only give off photons that have certain amounts of energy.
Isaac Newton thought that light was made of very small things that we would now call particles (he referred to them as "Corpuscles").
Christiaan Huygens thought that light was made of waves.
Scientists thought that a thing cannot be a particle and a wave at the same time.
Scientists did experiments to find out whether light was made of particles or waves.
They found out that both ideas were right — light was somehow both waves and particles.
The Double-slit experiment performed by Thomas Young showed that light must act like a wave.
The Photoelectric effect discovered by Albert Einstein proved that light had to act like particles that carried specific amounts of energy, and that the energies were linked to their frequencies.
This experimental result is called the "wave-particle duality" in quantum mechanics.
Later, physicists found out that everything behaves both like a wave and like a particle, not just light.
However, this effect is much smaller in large objects.
Here are some of the people who discovered the basic parts of quantum mechanics: Max Planck, Albert Einstein, Satyendra Nath Bose, Niels Bohr, Louis de Broglie, Max Born, Paul Dirac, Werner Heisenberg, Wolfgang Pauli, Erwin Schrödinger, John von Neumann, and Richard Feynman.
They did their work in the first half of the 20th century.
Beyond Planck
Quantum mechanics formulae and ideas were made to explain the light that comes from glowing hydrogen.
The quantum theory of the atom also had to explain why the electron stays in its orbit, which other ideas were not able to explain.
It followed from the older ideas that the electron would have to fall in to the center of the atom because it starts out being kept in orbit by its own energy, but it would quickly lose its energy as it revolves in its orbit. (
This is because electrons and other charged particles were known to emit light and lose energy when they changed speed or turned.)
Hydrogen lamps work like neon lights, but neon lights have their own unique group of colors (and frequencies) of light.
Scientists learned that they could identify all elements by the light colors they produce.
They just could not figure out how the frequencies were determined.
where B is a number that Balmer determined to be equal to 364.56 nm.
This equation only worked for the visible light from a hydrogen lamp.
But later, the equation was made more general:
where R is the Rydberg constant, equal to 0.0110 nm−1, and n must be greater than m.
Putting in different numbers for m and n, it is easy to predict frequencies for many types of light (ultraviolet, visible, and infared).
To see how this works, go to Hyperphysics and go down past the middle of the page. (
Use H = 1 for hydrogen.)
In 1908, Walter Ritz made the Ritz combination principle that shows how certain gaps between frequencies keep repeating themselves.
This turned out to be important to Werner Heisenberg several years later.
In 1905, Albert Einstein used Planck's idea to show that a beam of light is made up of a stream of particles called photons.
The energy of each photon depends on its frequency.
Einstein's idea is the beginning of the idea in quantum mechanics that all subatomic particles like electrons, protons, neutrons, and others are both waves and particles at the same time. (
See picture of atom with the electron as waves at atom.)
This led to a theory about subatomic particles and electromagnetic waves called wave-particle duality.
This is where particles and waves were neither one nor the other, but had certain properties of both.
In 1913, Niels Bohr came up with the idea that electrons could only take up certain orbits around the nucleus of an atom.
Under Bohr's theory, the numbers called m and n in the equation above could represent orbits.
Bohr's theory said electrons could begin in some orbit m and end up in some orbit n, or an electron could begin in some orbit n and end up in some orbit m so if a photon hits an electron, its energy will be absorbed, and the electron will move to a higher orbit because of that extra energy.
Under Bohr's theory, if an electron falls from a higher orbit to a lower orbit, then it will have to give up energy in the form of a photon.
The energy of the photon will equal the energy difference between the two orbits, and the energy of a photon makes it have a certain frequency and color.
Bohr's theory provided a good explanation of many aspects of subatomic phenomena, but failed to answer why each of the colors of light produced by glowing hydrogen (and by glowing neon or any other element) has a brightness of its own, and the brightness differences are always the same for each element.
Werner Heisenberg took on the job of explaining the brightness or "intensity" of each line.
He could not use any simple rule like the one Balmer had come up with.
He had to use the very difficult math of classical physics that figures everything out in terms of things like the mass (weight) of an electron, the charge (static electric strength) of an electron, and other tiny quantities.
Classical physics already had answers for the brightness of the bands of color that a hydrogen lamp produces, but the classical theory said that there should be a continuous rainbow, and not four separate color bands.
Heisenberg's explanation is:
There is some law that says what frequencies of light glowing hydrogen will produce.
It has to predict spaced-out frequencies when the electrons involved are moving between orbits close to the nucleus (center) of the atom, but it also has to predict that the frequencies will get closer and closer together as we look at what the electron does in moving between orbits farther and farther out.
It will also predict that the intensity differences between frequencies get closer and closer together as we go out.
Where classical physics already gives the right answers by one set of equations the new physics has to give the same answers but by different equations.
Classical physics uses the methods of the French mathematician Fourier to make a math picture of the physical world, and it uses collections of smooth curves that go together to make one smooth curve that gives, in this case, intensities for light of all frequencies from some light.
But it is not right because that smooth curve only appears at higher frequencies.
At lower frequencies, there are always isolated points and nothing connects the dots.
So, to make a map of the real world, Heisenberg had to make a big change.
He had to do something to pick out only the numbers that would match what was seen in nature.
Sometimes people say he "guessed" these equations, but he was not making blind guesses.
He found what he needed.
The numbers that he calculated would put dots on a graph, but there would be no line drawn between the dots.
And making one "graph" just of dots for every set of calculations would have wasted lots of paper and not have gotten anything done.
Heisenberg found a way to efficiently predict the intensities for different frequencies and to organize that information in a helpful way.
The rule says that when the electron moves from one orbit to another it either gains or loses energy, depending on whether it is getting farther from the center or nearer to it.
So we can put these orbits or energy levels in as headings along the top and the side of a grid.
For historical reasons the lowest orbit is called n, and the next orbit out is called n - a, then comes n - b, and so forth.
It is confusing that they used negative numbers when the electrons were actually gaining energy, but that is just the way it is.
Since the Rydberg rule gives us frequencies, we can use that rule to put in numbers depending on where the electron goes.
If the electron starts at n and ends up at n, then it has not really gone anywhere, so it did not gain energy and it did not lose energy.
So the frequency is 0.
If the electron starts at n-a and ends up at n, then it has fallen from a higher orbit to a lower orbit.
If it does so then it loses energy, and the energy it loses shows up as a photon.
The photon has a certain amount of energy, e, and that is related to a certain frequency f by the equation e = h f. So we know that a certain change of orbit is going to produce a certain frequency of light, f.  If the electron starts at n and ends up at n - a, that means it has gone from a lower orbit to a higher orbit.
That only happens when a photon of a certain frequency and energy comes in from the outside, is absorbed by the electron and gives it its energy, and that is what makes the electron go out to a higher orbit.
So, to keep everything making sense, we write that frequency as a negative number.
There was a photon with a certain frequency and now it has been taken away.
Heisenberg did not make the grids like this.
He just did the math that would let him get the intensities he was looking for.
But to do that he had to multiply two amplitudes (how high a wave measures) to work out the intensity. (
In classical physics, intensity equals amplitude squared.)
He made an odd-looking equation to handle this problem, wrote out the rest of his paper, handed it to his boss, and went on vacation.
Dr. Born looked at his funny equation and it seemed a little crazy.
He must have wondered, "Why did Heisenberg give me this strange thing?
Why does he have to do it this way?"
Then he realized that he was looking at a blueprint for something he already knew very well.
He was used to calling the grid or table that we could write by doing, for instance, all the math for frequencies, a matrix.
And Heisenberg's weird equation was a rule for multiplying two of them together.
Max Born was a very, very good mathematician.
He knew that since the two matrices (grids) being multiplied represented different things (like position (x,y,z) and momentum (mv), for instance), then when you multiply the first matrix by the second you get one answer and when you multiply the second matrix by the first matrix you get another answer.
Even though he did not know about matrix math, Heisenberg already saw this "different answers" problem and it had bothered him.
But Dr. Born was such a good mathematician that he saw that the difference between the first matrix multiplication and the second matrix multiplication was always going to involve Planck's constant, h, multiplied by the square root of negative one, i. So within a few days of Heisenberg's discovery they already had the basic math for what Heisenberg liked to call the "indeterminacy principle."
By "indeterminate" Heisenberg meant that something like an electron is just not pinned down until it gets pinned down.
It is a little like a jellyfish that is always squishing around and cannot be "in one place" unless you kill it.
Later, people got in the habit of calling it "Heisenberg's uncertainty principle," which made many people make the mistake of thinking that electrons and things like that are really "somewhere" but we are just uncertain about it in our own minds.
That idea is wrong.