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Amstrad CPC

The Amstrad CPC (short for "Colour Personal Computer") is a series of 8-bit home computers produced by Amstrad between 1984 and 1990. It was designed to compete in the mid-1980s home computer market dominated by the Commodore 64 and the ZX Spectrum, where it successfully established itself primarily in the United Kingdom, France, Spain, and the German-speaking parts of Europe.

The series spawned a total of six distinct models: The CPC 464, CPC 664, and CPC 6128 were highly successful competitors in the European home computer market. The later 464 plus and 6128 plus, intended to prolong the system's lifecycle with hardware updates, were considerably less successful, as was the attempt to repackage the plus hardware into a game console as the GX4000.

The CPC models' hardware is based on the Zilog Z80A CPU, complemented with either 64 or 128 KB of RAM. Their computer-in-a-keyboard design prominently features an integrated storage device, either a compact cassette deck or 3-inch floppy disk drive. The main units were only sold bundled with either a colour, green-screen or monochrome monitor that doubles as the main unit's power supply. Additionally, a wide range of first and third-party hardware extensions such as external disk drives, printers, and memory extensions, was available.

The CPC series was pitched against other home computers primarily used to play video games and enjoyed a strong supply of game software. The comparatively low price for a complete computer system with dedicated monitor, its high-resolution monochrome text and graphic capabilities and the possibility to run CP/M software also rendered the system attractive for business users, which was reflected by a wide selection of application software.

During its lifetime, the CPC series sold approximately three million units.

The original range
The philosophy behind the CPC series was twofold, firstly the concept was of an "all-in-one", where the computer, keyboard and its data storage device were combined in a single unit and sold with its own dedicated display monitor. Most home computers at that time such as ZX Spectrum series, Commodore 64, and BBC Micro relied on the use of the domestic television set and a separately connected tape recorder or disk drive. In itself, the all-in-one concept was not new, having been seen before on business-oriented machines and the Commodore PET.

Secondly, Amstrad founder Alan Sugar wanted the machine to resemble a "real computer, similar to what someone would see being used to check them in at the airport for their holidays", and for the machine to not look like "a pregnant calculator" – in reference presumably to the ZX81 and ZX Spectrum with their low cost, membrane-type keyboards.

CPC 464
The CPC 464 was one of the most successful computers in Europe and sold more than two million units.

The CPC 464 featured 64 KB RAM and an internal cassette deck. It was introduced in June 1984 in the UK. Initial suggested retail prices for the CPC 464 were £249.00/DM899.00 with a green screen and £359.00/DM1398.00 with a colour monitor. Following the introduction of the CPC 6128 in late 1985, suggested retail prices for the CPC 464 were cut by £50.00/DM100.00.

In 1990, the 464plus replaced the CPC 464 in the model line-up, and production of the CPC 464 was discontinued.

CPC 664

The CPC 664 features 64 KB RAM and an internal 3-inch floppy disk drive. It was introduced on 25 April 1985 in the UK. Initial suggested retail prices for the CPC 664 were £339.00/DM1198.00 with a green screen and £449.00/DM1998.00 with a colour monitor.

After the successful release of the CPC 464, consumers were constantly asking for two improvements: more memory and an internal disk drive. For Amstrad, the latter was easier to realise. At the deliberately low-key introduction of the CPC 664, the machine was positioned not only as the lowest-cost disk system but even the lowest-cost CP/M 2.2 machine. In the Amstrad CPC product range the CPC 664 complemented the CPC 464 which was neither discontinued nor reduced in price.

Compared to the CPC 464, the CPC 664's main unit has been significantly redesigned, not only to accommodate the floppy disk drive but also with a redesigned keyboard area. Touted as "ergonomic" by Amstrad's promotional material, the keyboard is noticeably tilted to the front with MSX-style cursor keys above the numeric keypad. Compared to the CPC 464's multicoloured keyboard, the CPC 664's keys are kept in a much quieter grey and pale blue colour scheme.

The back of the CPC 664 main unit features the same connectors as the CPC 464, with the exception of an additional 12V power lead. Unlike the CPC 464's cassette tape drive that could be powered off the main unit's 5V voltage, the CPC 664's floppy disk drive requires an additional 12V voltage. This voltage had to be separately supplied by an updated version of the bundled green screen/colour monitor (GT-65 and CTM-644 respectively).

The CPC 664 was only produced for approximately six months. In late 1985, when the CPC 6128 was introduced in Europe, Amstrad decided not to keep three models in the line-up, and production of the CPC 664 was discontinued.

CPC 6128
The CPC 6128 features 128 KB RAM and an internal 3-inch floppy disk drive. Aside from various hardware and firmware improvements, one of the CPC 6128's most prominent features is the compatibility with the CP/M+ operating system that rendered it attractive for business uses.

The CPC 6128 was released on 13 June 1985 and initially only sold in the US. Imported and distributed by Indescomp, Inc. of Chicago, it was the first Amstrad product to be sold in the United States, a market that at the time was traditionally hostile towards European computer manufacturers. Two months later, on 15 August 1985, it arrived in Europe and replaced the CPC 664 in the CPC model line-up. Initial suggested retail prices for the CPC 6128 were US$699.00/£299.00/DM1598.00 with a green screen and US$799.00/£399.00/DM2098.00 with a colour monitor.

In 1990, the 6128plus replaced the CPC 6128 in the model line-up, and production of the CPC 6128 was discontinued.

The plus range
In 1990, confronted with a changing home computer market, Amstrad decided to refresh the CPC model range by introducing a new range variantly labelled plus or PLUS, 1990, or CPC+ range. The main goals were numerous enhancements to the existing CPC hardware platform, to restyle the casework to provide a contemporary appearance, and to add native support of cartridge media. The new model palette includes three variants, the 464plus and 6128plus computers and the GX4000 video game console. The "CPC" abbreviation was dropped from the model names.

The redesign significantly enhanced the CPC hardware, mainly to rectify its previous shortcomings as a gaming platform. The redesigned video hardware allows for hardware sprites and soft scrolling, with a colour palette extended from a maximum of 16 colours (plus separately definable border) at one time from a choice of 27, increased to a maximum of 31 (16 for background and 15 for hardware sprites) out of 4096. The enhanced sound hardware offers automatic DMA transfer, allowing more complex sound effects with a significantly reduced processor overhead. Other hardware enhancements include the support of analogue joysticks, 8-bit printers, and ROM cartridges up to 4 Mbits.

The new range of models was intended to be completely backwards compatible with the original CPC models. Its enhanced features are only available after a deliberately obscure unlocking mechanism has been triggered, thus preventing existing CPC software from accidentally invoking them.

Despite the significant hardware enhancements, many viewed it as outdated, being based on an 8-bit CPU, and it failed to attract both customers and software producers who were moving towards systems such as the Amiga and Mega Drive which was launched a few short months after the plus range. The plus range was a commercial failure, and production was discontinued shortly after its introduction in 1990.

464 plus, 6128 plus
The 464 plus and 6128 plus models were intended as "more sophisticated and stylish" replacements of the CPC 464 and CPC 6128. Based on the redesigned plus hardware platform, they share the same base characteristics as their predecessors: The 464 plus is equipped with 64 KB RAM and a cassette tape drive, the 6128 plus features 128 KB RAM and a 3" floppy disk drive. Both models share a common case layout with a keyboard taken over from the CPC 6128 model, and the respective mass storage drive inserted in a case breakout.

In order to simplify the EMC screening process, the edge connectors of the previous models have been replaced with micro-ribbon connectors as previously used on the German Schneider CPC 6128. As a result, a wide range of extensions for the original CPC range are connector-incompatible with the 464 plus and 6128 plus. In addition, the 6128plus does not have a tape socket for an external tape drive.

The plus range is not equipped with an on-board ROM, and thus the 464 plus and the 6128 plus do not contain a firmware. Instead, Amstrad provided the firmware for both models via the ROM extension facility, contained on the included Burnin' Rubber and Locomotive BASIC cartridge. This resulted in reduced hardware localization cost (only some select key caps and case labels had to be localized) with the added benefit of a rudimentary copy protection mechanism (without a firmware present, the machine itself could not copy a game cartridge's content). As the enhanced V4 firmware's structural differences causes problems with some CPC software directly calling firmware functions by their memory addresses, Amstrad separately sold a cartridge containing the original CPC 6128's V3 firmware.

Both the 464 plus and the 6128 plus were introduced to the public in September 1990. Initial suggested retail prices were GB£229/1990 FRF with a monochrome monitor and GB£329/2990 FRF with a colour monitor for the 464 plus, and GB£329/2990 FRF with a monochrome monitor and GB£429/3990 FRF with a colour monitor for the 6128plus.

GX4000

Developed as part of the plus range, the GX4000 was Amstrad's short-lived attempt to enter the video game consoles market. Sharing the plus range's enhanced hardware characteristics, it represents the bare minimum variant of the range without a keyboard or support for mass storage devices. It came bundled with 2 paddle controllers and the racing game Burnin' Rubber.

CPC 472
During the August holidays of 1985, Spain briefly introduced an import tax of 15 000 pesetas (€90.15) on computers containing 64 KB or less of RAM (Royal Decree 1215/1985 and 1558/1985 ), and a new law (Royal Decree 1250/1985 ) mandated that all computers sold in Spain must have a Spanish keyboard. To circumvent this, Amstrad's Spanish distributor Indescomp (later to become Amstrad Spain) created and distributed the CPC 472, a modified version of the CPC 464. Its main differences are a small additional daughter board containing a CPC 664 ROM chip and an 8 KB memory chip, and a keyboard with a ñ key (although some of them were temporarily manufactured without the ñ key). The sole purpose of the 8 KB memory chip (which is not electrically connected to the machine, so consequently rendered unusable) is to increase the machine's total memory specs to 72 KB in order to circumvent the import tax. Some months later, Spain joined the European Communities by the Treaty of Accession 1985 and the import tax was suppressed, so Amstrad added the ñ key for the 464 and production of the CPC 472 was discontinued.

KC compact
The  ("Kleincomputer" - which means "small computer" - being a rather literal German translation of the English "microcomputer") is a clone of the Amstrad CPC built by East Germany's VEB Mikroelektronik Mühlhausen, part of VEB Kombinat Mikroelektronik Erfurt, in October 1989. Although the machine included various substitutes and emulations of an Amstrad CPC's hardware, the machine is largely compatible with Amstrad CPC software. It is equipped with 64 KB of memory and a CPC 6128's firmware customized to the modified hardware, including a copy of Locomotive BASIC 1.1 modified in the startup banner only. The expansion port is a K 1520 bus slot. The KC compact is the last 8-bit computer introduced in East Germany. Due to the German reunification happening at the time of the release only a very small number of systems were sold. The KC compact can be emulated by free software JKCEMU.

Aleste 520EX
In 1993, Omsk, Russia based company Patisonic released the Aleste 520EX, a computer highly compatible with the Amstrad CPC 6128. It could also be switched into an MSX mode. An expansion board named Magic Sound allowed to play Scream Tracker files.

Reception
A BYTE columnist in January 1985 called the CPC 464 "the closest yet to filling" his criteria for a useful home computer, including good keyboard, 80-column text, inexpensive disk drive, and support for a mainstream operating system like CP/M.

Processor
The entire CPC series is based on the Zilog Z80; a processor, clocked at 4 MHz.

In order to avoid the CPU and the video logic simultaneously accessing the shared main memory and causing video corruption ("snowing"), CPU memory access is constrained to occur on microsecond boundaries. This effectively pads every machine cycle to four clock cycles, causing a minor loss of processing power and resulting in what Amstrad estimated to be an "effective clock rate" of "approximately 3.3 MHz".

Memory
Amstrad CPCs are equipped with either 64 (CPC 464, CPC 664, 464plus, GX4000) or 128 (CPC 6128, 6128plus) KB of RAM. This base memory can be extended by up to 512 KB using memory expansions sold by third-party manufacturers, and by up to 4096 KB using experimental methods developed by hardware enthusiasts. Because the Z80 processor is only able to directly address 64 KB of memory, additional memory from the 128 KB models and memory expansions is made available using bank switching.

Video
Underlying a CPC's video output is the unusual pairing of a CRTC (Motorola 6845 or compatible) with a custom-designed gate array to generate a pixel display output. CPC 6128s later in production as well as the models from the plus range integrate both the CRTC and the gate array's functions with the system's ASIC.

Three built-in display resolutions are available: 160×200 pixels with 16 colours ("Mode 0", 20 text columns), 320×200 pixels with 4 colours ("Mode 1", 40 text columns), and 640×200 pixels with 2 colours ("Mode 2", 80 text columns). Increased screen size can be achieved by reprogramming the CRTC.

The original CPC video hardware supports a colour palette of 27 colours, generated from RGB colour space with each colour component assigned as either off, half on, or on (3 level RGB palette). The plus range extended the palette to 4096 colours, also generated from RGB with 4 bits each for red, green and blue (12-bit RGB).

With the exception of the GX4000, all CPC models lack an RF television or composite video output and instead shipped with a 6-pin RGB DIN connector, also used by Acorn computers, to connect the supplied Amstrad monitor. This connector delivers a 1v p-p analogue RGB with a 50 Hz composite sync signal that, if wired correctly, can drive a 50 Hz SCART television. External adapters for RF television were available as a first-party hardware accessory.

Audio
The CPC uses the General Instrument AY-3-8912 sound chip, providing three channels, each configurable to generate square waves, white noise or both. A small array of hardware volume envelopes are available.

Output is provided in mono by a small (4 cm) built-in loudspeaker with volume control, driven by an internal amplifier. Stereo output is provided through a 3.5 mm headphones jack.

It is possible to play back digital sound samples at a resolution of approximately 5-bit by sending a stream of values to the sound chip. This technique is very processor-intensive and hard to combine with any other processing. Examples are the title screens or other non-playable scenes of games like Chase H.Q., Meltdown, and RoboCop. The later Plus models incorporated a DMA engine in order to offload this processing.

Floppy disk drive
Amstrad uses Matsushita's 3" floppy disk drive [ref: CPCWiki], which was compatible with Hitachi's existing 3" floppy disk format. The chosen drive (built-in for later models) is a single-sided 40-track unit that requires the user to remove and flip the disk to access the other side. Each side has its own independent write-protect switch. The sides are termed "A" and "B", with each one commonly formatted to 180 KB (in AMSDOS format, comprising 2 KB directory and 178 KB storage) for a total of 360 KB per disk.

The interface with the drives is an NEC 765 FDC, used for the same purpose in the IBM PC/XT, PC/AT and PS/2 machines. Its features are not fully used in order to cut costs, namely DMA transfers and support for single density disks; they were formatted as double density using modified frequency modulation.

Discs were shipped in a paper sleeve or a hard plastic case resembling a compact disc "jewel" case. The casing is thicker and more rigid than that of 3.5 inch diskettes, and designed to be mailed without any additional packaging. A sliding metal cover to protect the media surface is internal to the casing and latched, unlike the simple external sliding cover of Sony's version. They were significantly more expensive than both 5.25 inch and 3.5 inch alternatives. This, combined with their low nominal capacities and their essentially proprietary nature, led to the format being discontinued shortly after the CPC itself was discontinued.

Apart from Amstrad's other 3-inch machines (the PCW and the ZX Spectrum +3), the few other computer systems to use them included the Sega SF-7000 and CP/M systems such as the Tatung Einstein and Osborne machines. They also found use on embedded systems.

The Shugart-standard interface means that Amstrad CPC machines are able to use standard 3", 3½" or 5¼" drives as their second drive. Programs such as ROMDOS and ParaDOS extend the standard AMSDOS system to provide support for double-sided, 80-track formats, enabling up to 800 KB to be stored on a single disk.

The 3-inch disks themselves are usually known as "discs" on the CPC, following the spelling on the machine's plastic casing and conventional British English spelling.

Expansion
The hardware and firmware was designed to be able to access software provided on external ROMs. Each ROM has to be a 16 KB block and is switched in and out of the memory space shared with the video RAM. The Amstrad firmware is deliberately designed so that new software could be easily accessed from these ROMs. Popular applications were marketed on ROM, particularly word processing and programming utility software (examples are Protext and Brunword of the former, and the MAXAM assembler of the latter type).

Such extra ROM chips do not plug directly into the CPC itself, but into extra plug-in "rom boxes" which contain sockets for the ROM chips and a minimal amount of decoding circuitry for the main machine to be able to switch between them. These boxes were either marketed commercially or could be built by competent hobbyists and they attached to the main expansion port at the back of the machine. Software on ROM loads much faster than from disc or tape and the machine's boot-up sequence was designed to evaluate ROMs it found and optionally hand over control of the machine to them. This allows significant customisation of the functionality of the machine, something that enthusiasts exploited for various purposes. However, the typical users would probably not be aware of this added ROM functionality unless they read the CPC press, as it is not described in the user manual and was hardly ever mentioned in marketing literature. It is, however, documented in the official Amstrad firmware manual.

The machines also feature a 9-pin Atari joystick port that will either directly take one joystick, or two joysticks by use of a splitter cable.

RS232 serial adapters
Amstrad issued two RS-232-C D25 serial interfaces, attached to the expansion connector on the rear of the machine, with a through-connector for the CPC 464 disk drive or other peripherals.

The original interface came with a Book of Spells for facilitating data transfer between other systems using a proprietary protocol in the device's own ROM, as well as terminal software to connect to British Telecom's Prestel service. A separate version of the ROM was created for the U.S. market due to the use of the commands "|SUCK" and "|BLOW", which were considered unacceptable there.

Software and hardware limitations in this interface led to its replacement with an Amstrad-branded version of a compatible alternative by Pace. Serial interfaces were also available from third-party vendors such as KDS Electronics and Cirkit.

BASIC and operating system
Like most home computers at the time, the CPC has its OS and a BASIC interpreter built in as ROM. It uses Locomotive BASIC - an improved version of Locomotive Software's Z80 BASIC for the BBC Micro co-processor board. It is particularly notable for providing easy access to the machine's video and audio resources in contrast to the POKE commands required on generic Microsoft implementations. Other unusual features include timed event handling with the AFTER and EVERY commands, and text-based windowing.

CP/M
Digital Research's CP/M operating system was supplied with the 664 and 6128 disk-based systems, and the DDI-1 disk expansion unit for the 464. 64k machines shipped with CP/M 2.2 alone, while the 128k machines also include CP/M 3.1. The compact CP/M 2.2 implementation is largely stored on the boot sectors of a 3" disk in what was called "System format"; typing |CPM from Locomotive BASIC would load code from these sectors, making it a popular choice for custom game loading routines. The CP/M 3.1 implementation is largely in a separate file which is in turn loaded from the boot sector. Much public domain CP/M software was made available for the CPC, from word-processors such as VDE to complete bulletin board systems such as ROS.

Other languages
Although it was possible to obtain compilers for Locomotive BASIC, C and Pascal, the majority of the CPC's software was written in native Z80 assembly language. Popular assemblers were Hisoft's Devpac, Arnor's Maxam, and (in France) DAMS. Disk-based CPC (not Plus) systems shipped with an interpreter for the educational language LOGO, booted from CP/M 2.2 but largely CPC-specific with much code resident in the AMSDOS ROM; 6128 machines also include a CP/M 3.1, non-ROM version. A C compiler was also written and made available for the European market through Tandy Europe, by Micro Business products.

Roland
In an attempt to give the CPC a recognisable mascot, a number of games by Amstrad's in-house software publisher Amsoft have been tagged with the Roland name. However, as the games had not been designed around the Roland character and only had the branding added later, the character design varies immensely, from a spiky-haired blonde teenager (Roland Goes Digging) to a white cube with legs (Roland Goes Square Bashing) or a mutant flea (Roland in the Caves). The only two games with similar gameplay and main character design are Roland in Time and its sequel Roland in Space. The Roland character was named after Roland Perry, one of the lead designers of the original CPC range.

Schneider Computer Division
In order to market its computers in Germany, Austria, and Switzerland where Amstrad did not have any distribution structures, Amstrad entered a partnership with Schneider Rundfunkwerke AG, a German company that - very much like Amstrad itself - was previously only known for value-priced audio products. In 1984, Schneider's Schneider Computer Division daughter company was created specifically for the task, and the complete Amstrad CPC line-up was branded and sold as Schneider CPC.

Although they are based on the same hardware, the Schneider CPC models differ from the Amstrad CPC models in several details. Most prominently, the Schneider CPC 464 and CPC 664 keyboards featured grey instead of coloured keys, but still in the original British keyboard layout. To achieve a German "QWERTZ" keyboard layout, Schneider marketed a small software program to reassign the keys as well as sticker labels for the keys. In order to conform with stricter German EMC regulations, the complete Schneider CPC line-up is equipped with an internal metal shielding. For the same reason, the Schneider CPC 6128 features micro ribbon type connectors instead of edge connectors. Both the greyscale keyboard and the micro ribbon connectors found their way up into the design of later Amstrad CPC models.

In 1988, after Schneider refused to market Amstrad's AT-compatible computer line, the cooperation ended. Schneider went on to sell the remaining stock of Schneider CPC models and used their now well-established market position to introduce its own PC designs. With the formation of its German daughter company Amstrad GmbH to distribute its product lines including the CPC 464 and CPC 6128, Amstrad attempted but ultimately failed to establish their own brand in the German-speaking parts of Europe.

Community
The Amstrad CPC enjoyed a strong and long lifetime, mainly due to the machines use for businesses as well as gaming. Dedicated programmers continued working on the CPC range, even producing graphical user interface (GUI) operating systems such as SymbOS. Internet sites devoted to the CPC have appeared from around the world featuring forums, news, hardware, software, programming and games. CPC Magazines appeared during the 1980s including publications in countries such as Britain, France, Spain, Germany, Denmark, Australia, and Greece. Titles included the official Amstrad Computer User publication, as well as independent titles like Amstrad Action, Amtix!, Computing with the Amstrad CPC, CPC Attack, Australia's The Amstrad User, France's Amstrad Cent Pour Cent and Amstar. Following the CPC's end of production, Amstrad gave permission for the CPC ROMs to be distributed freely as long as the copyright message is not changed and that it is acknowledged that Amstrad still holds copyright, giving emulator authors the possibility to ship the CPC firmware with their programs.

Influence on other Amstrad machines
Amstrad followed their success with the CPC 464 by launching the Amstrad PCW word-processor range, another Z80-based machine with a 3" disk drive and software by Locomotive Software. The PCW was originally developed to be partly compatible with an improved version of the CPC (ANT, or Arnold Number Two - the CPC's development codename was Arnold). However, Amstrad decided to focus on the PCW, and the ANT project never came to market.

On 7 April 1986, Amstrad announced it had bought from Sinclair Research "...the worldwide rights to sell and manufacture all existing and future Sinclair computers and computer products, together with the Sinclair brand name and those intellectual property rights where they relate to computers and computer-related products." which included the ZX Spectrum, for £5 million. This included Sinclair's unsold stock of Sinclair QLs and Spectrums. Amstrad made more than £5 million on selling these surplus machines alone. Amstrad launched two new variants of the Spectrum: the ZX Spectrum +2, based on the ZX Spectrum 128, with a built-in tape drive (like the CPC 464) and, the following year, the ZX Spectrum +3, with a built-in floppy disk drive (similar to the CPC 664 and 6128), taking the 3" discs that Amstrad CPC machines used.

title: Amstrad CPC


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Abdulaziz al-Omari

Abdulaziz al-Omari (عبد العزيز العُمري, ʿAbd al-ʿAzīz al-ʿUmarī, also transliterated as Alomari or al-Umari; 28 May 1979 – 11 September 2001) was a Saudi terrorist who was one of five hijackers of American Airlines Flight 11 as part of the September 11 attacks in 2001.

Prior to the attacks, al-Omari was an imam at his mosque in Saudi Arabia's al-Qassim province. He arrived in the United States in June 2001 on a tourist visa, obtained through the Visa Express program. On September 11, 2001, al-Omari boarded American Airlines Flight 11 and assisted in the hijacking of the plane, which was crashed into the North Tower of the World Trade Center, as part of the coordinated attacks.

Early life and career
Abdulaziz al-Omari was from the poor Saudi Arabian province of Asir, along with his fellow hijackers in the September 11 attacks, brothers Wail and Waleed al-Shehri. It is alleged he graduated with honors from high school. He attained a degree from Imam Muhammad ibn Saud Islamic University, got married, and had a daughter briefly before the attacks. He taught as an imam at his mosque in al-Qassim province, which was the "heartland" of Wahhabism, a strict form of Islam. At the mosque, which experts refer to as a "terrorist factory", he was possibly taught by the radical cleric Sulayman al Alwan.

According to Walid bin Attash, al-Omari was one of a group of future hijackers who provided security at Kandahar airport after their basic training at an al-Qaeda camp. During the 2000 Al Qaeda Summit in Kuala Lumpur, American authorities state that immigration records show that a person named Abdulaziz al-Omari was visiting the country, although they say they are not sure that this was the same person.

Early 2001
al-Omari eventually became involved in the planning for the September 11 attacks on the United States, an idea formulated by Osama bin Laden. The attacks involved hijacking commercial airplanes and crashing them into buildings; al-Omari would hijack American Airlines Flight 11, which would crash into the World Trade Center in New York City. At the time of the hijacking, al-Omari was 22. In the autumn of 2001, after the attacks, al Jazeera television broadcast a tape they claim was made by him. The speaker made a farewell suicide video. In it he read, "I am writing this with my full conscience and I am writing this in expectation of the end, which is near... God praise everybody who trained and helped me, namely the leader Sheikh Osama bin Laden."

al-Omari and hijacker Salem al-Hazmi entered the United States through a Dubai flight on June 29, 2001, landing in New York City. al-Omari had used the controversial Visa Express program to gain entry. The two were probably picked up by Salem's brother, Nawaf al-Hazmi, on the 30th; this is assumed because of a recorded traffic accident by Nawaf on George Washington Bridge that day. al-Omari likely stayed with several other hijackers in Paterson, New Jersey (where he rented a mailbox ), before moving to his own place in Vero Beach, Florida. On his rental agreement form for that house, al-Omari gave two license-plates authorized to park in his space, one of which was registered to Mohamed Atta, the attacks' mastermind. al-Omari obtained a fake United States ID card from All Services Plus in Passaic County, New Jersey, which was in the business of selling fake documents; another was given to Khalid al-Mihdhar. The employee who gave them the IDs claimed he had no idea they were "anything more [than ordinary] customers". Atta bought tickets for Flight 11 for himself and al-Omari on August 28. On September 6, al-Omari and fellow hijacker Satam al-Suqami flew from Florida to Boston to stay at the Park Inn Hotel.

September 10
On September 10, 2001, Atta picked up al-Omari from the Park Inn Hotel, and the two drove to South Portland, Maine, in a rented Nissan Altima. Some sources state there is no evidence as to why they went to Portland, whereas ABC News says it was a last-minute decision by Atta to stagger the Flight 11 hijackers' entrances into Logan International Airport on the 11th. Multiple people have claimed to see Atta and other hijackers in Portland that summer, but the FBI has found no evidence of this. On the 10th, Atta and al-Omari purchased a room (233) at the town's Comfort Inn. They did not ask for a wake-up call. Their luggage included a folding knife, "a videocassette [about] a Boeing 757 flight simulator, pepper spray, Atta’s will, [and Atta's] handwritten instructions to his 18 fellow hijackers"; American Airlines Flight 11 was a Boeing 767.

They stayed in their hotel room for two hours, until 8 p.m., when al-Omari made a four-minute phone call from a nearby Pizza Hut's pay phone to a phone belonging to Marwan al-Shehhi, who would hijack United Airlines Flight 175. Five minutes later, at a restaurant named Pizzeria Uno, the two withdrew $80 from an ATM. They then drove back to the Pizza Hut, where a second pay phone call was placed at 8:50. They decided to go to Walmart, but got lost and went to a gas station to ask for directions. In a video recorded at the gas station, Atta has a piece of paper in his hand and shows it to al-Omari, and then they leave. At the Walmart, the two purchased a six-volt battery converter for an unknown reason. Staff of the Walmart said that weeks earlier, Atta had bought a box cutter there, but this is uncorroborated. The two then returned to the Comfort Inn, where they stayed for hours.

Day of the attacks
At 5:33 a.m. on September 11, al-Omari and Atta checked out of the hotel. al-Omari made another cash withdrawal at the Pizzeria Uno ATM, and then the two went to Portland International Jetport. At around 5:40, the two spoke with a ticket agent, who raised no suspicions about them. Both men boarded their flight, which landed in Logan International Airport at 6:45. Eight other hijackers were waiting at the airport. It is unknown why this connecting flight through Portland happened, especially because the two almost missed their flight at Logan. Their flight, American 11, was supposed to fly to Los Angeles.

Atta and al-Omari then boarded Flight 11 with fellow hijackers Satam al-Suqami, Wail al-Shehri, and Waleed al-Shehri. The other hijackers at the airport went on United Airlines Flight 175. al-Omari's passport, which would identify him as a hijacker to investigators later, was in the two men's aforementioned luggage; this luggage was accidentally left at Portland International Airport, failing to make it onto the connecting flight to Logan. The two men probably decided they did not need the luggage's folding knife and pepper spray in their attacks. Atta and al-Omari had seats next to each other in first class, row 8, on Flight 11. The flight left the Logan runway at 7:59. The hijackers took over the plane starting at 8:14, when multiple passengers were maced and stabbed. Atta then commanded the plane's controls, and at 8:37, the plane began a rapid descent. At 8:46, it was crashed into the World Trade Center's North Tower, and everyone onboard was killed. Floors 93 to 99 were impacted, and many inside died.

Aftermath
Controversy over the identity of al-Omari erupted shortly after the attacks. At first, the FBI had named Abdul Rahman al-Omari, a pilot for Saudi Arabian Airlines, as the pilot of Flight 11. It was quickly shown that this person was still alive, and the FBI issued an apology. It was also quickly determined that Mohamed Atta was the pilot among the hijackers. The FBI then named Abdulaziz al-Omari as a hijacker. A man with the same name as those given by the FBI turned up alive in Saudi Arabia, saying that he had studied at the University of Denver and his passport was stolen there in 1995. The name, origin, birth date, and occupation were released by the FBI, but the picture was not of him. "I couldn't believe it when the FBI put me on their list", he said. "They gave my name and my date of birth, but I am not a suicide bomber. I am here. I am alive. I have no idea how to fly a plane. I had nothing to do with this."

The FBI gave a press conference on October 5, 2001, where they gave details regarding Atta and the real al-Omari's movements on September 10 and 11.

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: Abdulaziz al-Omari


text:
Aage Bohr

Aage Niels Bohr (19 June 1922 – 8 September 2009) was a Danish nuclear physicist who shared the Nobel Prize in Physics in 1975 with Ben Roy Mottelson and James Rainwater "for the discovery of the connection between collective motion and particle motion in atomic nuclei and the development of the theory of the structure of the atomic nucleus based on this connection". His father was Niels Bohr.

Starting from Rainwater's concept of an irregular-shaped liquid drop model of the nucleus, Bohr and Mottelson developed a detailed theory that was in close agreement with experiments.

Since his father, Niels Bohr, had won the prize in 1922, he and his father are one of the six pairs of fathers and sons who have both won the Nobel Prize and one of the four pairs who have both won the Nobel Prize in Physics.

Early life and education
Bohr was born in Copenhagen on 19 June 1922, the fourth of six sons of the physicist Niels Bohr and his wife Margrethe Bohr (née Nørlund). His oldest brother, Christian, died in a boating accident in 1934, and his youngest, Harald, was severely disabled and placed away from the home in Copenhagen at the age of four. He would later die from childhood meningitis. Of the others, Hans became a physician; Erik, a chemical engineer; and Ernest, a lawyer and Olympic athlete who played field hockey for Denmark at the 1948 Summer Olympics in London. The family lived at the Institute of Theoretical Physics at the University of Copenhagen, now known as the Niels Bohr Institute, where he grew up surrounded by physicists who were working with his father, such as Hans Kramers, Oskar Klein, Yoshio Nishina, Wolfgang Pauli and Werner Heisenberg. In 1932, the family moved to the Carlsberg Æresbolig, a mansion donated by Carl Jacobsen, the heir to Carlsberg breweries, to be used as an honorary residence by the Dane who had made the most prominent contribution to science, literature, or the arts.

Bohr went to high school at Sortedam Gymnasium in Copenhagen. In 1940, shortly after the German occupation of Denmark in April, he entered the University of Copenhagen, where he studied physics. He assisted his father, helping draft correspondence and articles related to epistemology and physics. In September 1943, word reached his family that the Nazis considered them to be Jewish, because Bohr's grandmother, Ellen Adler Bohr, had been Jewish, and that they therefore were in danger of being arrested. The Danish resistance helped the family escape by sea to Sweden. Bohr arrived there in October 1943, and then flew to Britain on a de Havilland Mosquito operated by British Overseas Airways Corporation. The Mosquitoes were unarmed high-speed bomber aircraft that had been converted to carry small, valuable cargoes or important passengers. By flying at high speed and high altitude, they could cross German-occupied Norway, and yet avoid German fighters. Bohr, equipped with parachute, flying suit and oxygen mask, spent the three-hour flight lying on a mattress in the aircraft's bomb bay.

On arrival in London, Bohr rejoined his father, who had flown to Britain the week before. He officially became a junior researcher at the Department of Scientific and Industrial Research, but actually served as personal assistant and secretary to his father. The two worked on Tube Alloys, the British atomic bomb project. On 30 December 1943, they made the first of a number of visits to the United States, where his father was a consultant to the Manhattan Project. Due to his father's fame, they were given false names; Bohr became James Baker, and his father, Nicholas Baker. In 1945, the director of the Los Alamos Laboratory, J. Robert Oppenheimer, asked them to review the design of the modulated neutron initiator. They reported that it would work. That they had reached this conclusion put Enrico Fermi's concerns about the viability of the design to rest. The initiators performed flawlessly in the bombs used in the atomic bombings of Hiroshima and Nagasaki in August 1945.

Career
In August 1945, with the war ended, Bohr returned to Denmark, where he resumed his university education, graduating with a master's degree in 1946, with a thesis concerned with some aspects of atomic stopping power problems. In early 1948, Bohr became a member of the Institute for Advanced Study in Princeton, New Jersey. While paying a visit to Columbia University, he met Isidor Isaac Rabi, who sparked in him an interest in recent discoveries related to the hyperfine structure of deuterium. This led to Bohr becoming a visiting fellow at Columbia from January 1949 to August 1950. While in the United States, Bohr married Marietta Soffer on 11 March 1950. They had three children: Vilhelm, Tomas and Margrethe.

By the late 1940s it was known that the properties of atomic nuclei could not be explained by then-current models such as the liquid drop model developed by Niels Bohr amongst others. The shell model, developed in 1949 by Maria Goeppert Mayer and others, allowed some additional features to be explained, in particular the so-called magic numbers. However, there were also properties that could not be explained, including the non-spherical distribution of charge in certain nuclei. In a 1950 paper, James Rainwater of Columbia University suggested a variant of the drop model of the nucleus that could explain a non-spherical charge distribution. Rainwater's model postulated a nucleus like a balloon with balls inside that distort the surface as they move about. He discussed the idea with Bohr, who was visiting Columbia at the time, and had independently conceived the same idea, and had, about a month after Rainwater's submission, submitted for publication a paper that discussed the same problem, but along more general lines. Bohr imagined a rotating, irregular-shaped nucleus with a form of surface tension. Bohr developed the idea further, in 1951 publishing a paper that comprehensively treated the relationship between oscillations of the surface of the nucleus and the movement of the individual nucleons.

Upon his return to Copenhagen in 1950, Bohr began working with Ben Roy Mottelson to compare the theoretical work with experimental data. In three papers, that were published in 1952 and 1953, Bohr and Mottelson demonstrated close agreement between theory and experiment; for example, showing that the energy levels of certain nuclei could be described by a rotation spectrum. They were thereby able to reconcile the shell model with Rainwater's concept. This work stimulated many new theoretical and experimental studies. Bohr, Mottelson and Rainwater were jointly awarded the 1975 Nobel Prize in Physics "for the discovery of the connection between collective motion and particle motion in atomic nuclei and the development of the theory of the structure of the atomic nucleus based on this connection". Because his father had been awarded the prize in 1922, Bohr became one of only four pairs of fathers and sons to win the Nobel Prize in Physics.

Only after doing his Nobel Prize-winning research did Bohr receive his doctorate from the University of Copenhagen, in 1954, writing his thesis on "Rotational States of Atomic Nuclei". Bohr became a professor at the University of Copenhagen in 1956, and, following his father's death in 1962, succeeded him as director of the Niels Bohr Institute, a position he held until 1970. He remained active there until he retired in 1992. He was also a member of the board of the Nordic Institute for Theoretical Physics from its inception in 1957, and was its director from 1975 to 1981. In addition to the Nobel Prize, he won the Dannie Heineman Prize for Mathematical Physics in 1960, the Atoms for Peace Award in 1969, H. C. Ørsted Medal in 1970, Rutherford Medal and Prize in 1972, John Price Wetherill Medal in 1974, and the Ole Rømer medal in 1976. Bohr and Mottelson continued to work together, publishing a two-volume monograph, Nuclear Structure. The first volume, Single-Particle Motion, appeared in 1969; the second, Nuclear Deformations, in 1975.

In 1972 Bohr was awarded an honorary degree, doctor philos. honoris causa, at the Norwegian Institute of Technology, later part of Norwegian University of Science and Technology. He was a member of the Norwegian Academy of Science and Letters from 1980. Bohr was also an elected member of the American Academy of Arts and Sciences, the American Philosophical Society, and the United States National Academy of Sciences.

In 1981, Bohr became a founding member of the World Cultural Council.

Bohr's wife Marietta died on 2 October 1978. In 1981, he married Bente Scharff Meyer (1926–2011). His son, Tomas Bohr, is a professor of physics at the Technical University of Denmark, working in the area of fluid dynamics. Aage Bohr died in Copenhagen on 9 September 2009. He was survived by his second wife and children.

Bohr's Nobel Prize medal was sold at auction in November 2011. It was subsequently sold at auction in April 2019 for $90,000.

title: Aage Bohr


text:
Analytic geometry

In mathematics, analytic geometry, also known as coordinate geometry or Cartesian geometry, is the study of geometry using a coordinate system. This contrasts with synthetic geometry.

Analytic geometry is used in physics and engineering, and also in aviation, rocketry, space science, and spaceflight. It is the foundation of most modern fields of geometry, including algebraic, differential, discrete and computational geometry.

Usually the Cartesian coordinate system is applied to manipulate equations for planes, straight lines, and circles, often in two and sometimes three dimensions. Geometrically, one studies the Euclidean plane (two dimensions) and Euclidean space. As taught in school books, analytic geometry can be explained more simply: it is concerned with defining and representing geometric shapes in a numerical way and extracting numerical information from shapes' numerical definitions and representations. That the algebra of the real numbers can be employed to yield results about the linear continuum of geometry relies on the Cantor–Dedekind axiom.

Ancient Greece
The Greek mathematician Menaechmus solved problems and proved theorems by using a method that had a strong resemblance to the use of coordinates and it has sometimes been maintained that he had introduced analytic geometry.

Apollonius of Perga, in On Determinate Section, dealt with problems in a manner that may be called an analytic geometry of one dimension; with the question of finding points on a line that were in a ratio to the others. Apollonius in the Conics further developed a method that is so similar to analytic geometry that his work is sometimes thought to have anticipated the work of Descartes by some 1800 years. His application of reference lines, a diameter and a tangent is essentially no different from our modern use of a coordinate frame, where the distances measured along the diameter from the point of tangency are the abscissas, and the segments parallel to the tangent and intercepted between the axis and the curve are the ordinates. He further developed relations between the abscissas and the corresponding ordinates that are equivalent to rhetorical equations (expressed in words) of curves. However, although Apollonius came close to developing analytic geometry, he did not manage to do so since he did not take into account negative magnitudes and in every case the coordinate system was superimposed upon a given curve a posteriori instead of a priori. That is, equations were determined by curves, but curves were not determined by equations. Coordinates, variables, and equations were subsidiary notions applied to a specific geometric situation.

Persia
The 11th-century Persian mathematician Omar Khayyam saw a strong relationship between geometry and algebra and was moving in the right direction when he helped close the gap between numerical and geometric algebra with his geometric solution of the general cubic equations, but the decisive step came later with Descartes. Omar Khayyam is credited with identifying the foundations of algebraic geometry, and his book Treatise on Demonstrations of Problems of Algebra (1070), which laid down the principles of analytic geometry, is part of the body of Persian mathematics that was eventually transmitted to Europe. Because of his thoroughgoing geometrical approach to algebraic equations, Khayyam can be considered a precursor to Descartes in the invention of analytic geometry.

Western Europe
Analytic geometry was independently invented by René Descartes and Pierre de Fermat, although Descartes is sometimes given sole credit. Cartesian geometry, the alternative term used for analytic geometry, is named after Descartes.

Descartes made significant progress with the methods in an essay titled La Géométrie (Geometry), one of the three accompanying essays (appendices) published in 1637 together with his Discourse on the Method for Rightly Directing One's Reason and Searching for Truth in the Sciences, commonly referred to as Discourse on Method.

La Geometrie, written in his native French tongue, and its philosophical principles, provided a foundation for calculus in Europe. Initially the work was not well received, due, in part, to the many gaps in arguments and complicated equations. Only after the translation into Latin and the addition of commentary by van Schooten in 1649 (and further work thereafter) did Descartes's masterpiece receive due recognition.

Pierre de Fermat also pioneered the development of analytic geometry. Although not published in his lifetime, a manuscript form of Ad locos planos et solidos isagoge (Introduction to Plane and Solid Loci) was circulating in Paris in 1637, just prior to the publication of Descartes' Discourse. Clearly written and well received, the Introduction also laid the groundwork for analytical geometry. The key difference between Fermat's and Descartes' treatments is a matter of viewpoint: Fermat always started with an algebraic equation and then described the geometric curve that satisfied it, whereas Descartes started with geometric curves and produced their equations as one of several properties of the curves. As a consequence of this approach, Descartes had to deal with more complicated equations and he had to develop the methods to work with polynomial equations of higher degree. It was Leonhard Euler who first applied the coordinate method in a systematic study of space curves and surfaces.

Coordinates

In analytic geometry, the plane is given a coordinate system, by which every point has a pair of real number coordinates. Similarly, Euclidean space is given coordinates where every point has three coordinates. The value of the coordinates depends on the choice of the initial point of origin. There are a variety of coordinate systems used, but the most common are the following:

Cartesian coordinates (in a plane or space)
The most common coordinate system to use is the Cartesian coordinate system, where each point has an x-coordinate representing its horizontal position, and a y-coordinate representing its vertical position. These are typically written as an ordered pair (x, y). This system can also be used for three-dimensional geometry, where every point in Euclidean space is represented by an ordered triple of coordinates (x, y, z).

Polar coordinates (in a plane)
In polar coordinates, every point of the plane is represented by its distance r from the origin and its angle θ, with θ normally measured counterclockwise from the positive x-axis. Using this notation, points are typically written as an ordered pair (r, θ). One may transform back and forth between two-dimensional Cartesian and polar coordinates by using these formulae: $$x = r\, \cos\theta,\, y = r\, \sin\theta; \, r = \sqrt{x^2+y^2},\, \theta = \arctan(y/x).$$ This system may be generalized to three-dimensional space through the use of cylindrical or spherical coordinates.

Cylindrical coordinates (in a space)
In cylindrical coordinates, every point of space is represented by its height z, its radius r from the z-axis and the angle θ its projection on the xy-plane makes with respect to the horizontal axis.

Spherical coordinates (in a space)
In spherical coordinates, every point in space is represented by its distance ρ from the origin, the angle θ its projection on the xy-plane makes with respect to the horizontal axis, and the angle φ that it makes with respect to the z-axis. The names of the angles are often reversed in physics.

Equations and curves
In analytic geometry, any equation involving the coordinates specifies a subset of the plane, namely the solution set for the equation, or locus. For example, the equation y = x corresponds to the set of all the points on the plane whose x-coordinate and y-coordinate are equal. These points form a line, and y = x is said to be the equation for this line. In general, linear equations involving x and y specify lines, quadratic equations specify conic sections, and more complicated equations describe more complicated figures.

Usually, a single equation corresponds to a curve on the plane. This is not always the case: the trivial equation x = x specifies the entire plane, and the equation x2 + y2 = 0 specifies only the single point (0, 0). In three dimensions, a single equation usually gives a surface, and a curve must be specified as the intersection of two surfaces (see below), or as a system of parametric equations. The equation x2 + y2 = r2 is the equation for any circle centered at the origin (0, 0) with a radius of r.

Lines and planes
Lines in a Cartesian plane, or more generally, in affine coordinates, can be described algebraically by linear equations. In two dimensions, the equation for non-vertical lines is often given in the slope-intercept form: $$ y = mx + b $$ where:
 * m is the slope or gradient of the line.
 * b is the y-intercept of the line.
 * x is the independent variable of the function y = f(x).

In a manner analogous to the way lines in a two-dimensional space are described using a point-slope form for their equations, planes in a three dimensional space have a natural description using a point in the plane and a vector orthogonal to it (the normal vector) to indicate its "inclination".

Specifically, let $$\mathbf{r}_0$$ be the position vector of some point $$P_0 = (x_0,y_0,z_0)$$, and let $$\mathbf{n} = (a,b,c)$$ be a nonzero vector. The plane determined by this point and vector consists of those points $$P$$, with position vector $$\mathbf{r}$$, such that the vector drawn from $$P_0$$ to $$P$$ is perpendicular to $$\mathbf{n}$$. Recalling that two vectors are perpendicular if and only if their dot product is zero, it follows that the desired plane can be described as the set of all points $$\mathbf{r}$$ such that $$\mathbf{n} \cdot (\mathbf{r}-\mathbf{r}_0) =0.$$ (The dot here means a dot product, not scalar multiplication.) Expanded this becomes $$ a (x-x_0)+ b(y-y_0)+ c(z-z_0)=0,$$ This is just a linear equation: $$ ax + by + cz + d = 0, \text{ where } d = -(ax_0 + by_0 + cz_0).$$ Conversely, it is easily shown that if a, b, c and d are constants and a, b, and c are not all zero, then the graph of the equation $$ ax + by + cz + d = 0,$$ This familiar equation for a plane is called the general form of the equation of the plane.

In three dimensions, lines can not be described by a single linear equation, so they are frequently described by parametric equations: $$ x = x_0 + at $$ $$ y = y_0 + bt $$ $$ z = z_0 + ct $$ where:
 * x, y, and z are all functions of the independent variable t which ranges over the real numbers.
 * (x0, y0, z0) is any point on the line.
 * a, b, and c are related to the slope of the line, such that the vector (a, b, c) is parallel to the line.

Conic sections
In the Cartesian coordinate system, the graph of a quadratic equation in two variables is always a conic section – though it may be degenerate, and all conic sections arise in this way. The equation will be of the form $$Ax^2 + Bxy + Cy^2 +Dx + Ey + F = 0\text{ with }A, B, C\text{ not all zero.} $$ As scaling all six constants yields the same locus of zeros, one can consider conics as points in the five-dimensional projective space $$\mathbf{P}^5.$$

The conic sections described by this equation can be classified using the discriminant

$$B^2 - 4AC .$$ If the conic is non-degenerate, then:
 * if $$B^2 - 4AC < 0 $$, the equation represents an ellipse;
 * if $$A = C $$ and $$B = 0 $$, the equation represents a circle, which is a special case of an ellipse;
 * if $$B^2 - 4AC = 0 $$, the equation represents a parabola;
 * if $$B^2 - 4AC > 0 $$, the equation represents a hyperbola;
 * if we also have $$A + C = 0 $$, the equation represents a rectangular hyperbola.

Quadric surfaces
A quadric, or quadric surface, is a 2-dimensional surface in 3-dimensional space defined as the locus of zeros of a quadratic polynomial. In coordinates x1, x2,x3, the general quadric is defined by the algebraic equation

$$\sum_{i,j=1}^{3} x_i Q_{ij} x_j + \sum_{i=1}^{3} P_i x_i + R = 0.$$

Quadric surfaces include ellipsoids (including the sphere), paraboloids, hyperboloids, cylinders, cones, and planes.

Distance and angle

In analytic geometry, geometric notions such as distance and angle measure are defined using formulas. These definitions are designed to be consistent with the underlying Euclidean geometry. For example, using Cartesian coordinates on the plane, the distance between two points (x1, y1) and (x2, y2) is defined by the formula $$d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2},$$ which can be viewed as a version of the Pythagorean theorem. Similarly, the angle that a line makes with the horizontal can be defined by the formula $$\theta = \arctan(m),$$ where m is the slope of the line.

In three dimensions, distance is given by the generalization of the Pythagorean theorem: $$d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2+ (z_2 - z_1)^2},$$ while the angle between two vectors is given by the dot product. The dot product of two Euclidean vectors A and B is defined by $$\mathbf A\cdot\mathbf B \stackrel{\mathrm{def}}{=} \left\|\mathbf A\right\| \left\|\mathbf B\right\| \cos\theta,$$ where θ is the angle between A and B.

Transformations

Transformations are applied to a parent function to turn it into a new function with similar characteristics.

The graph of $$R(x,y)$$ is changed by standard transformations as follows:
 * Changing $$x$$ to $$x-h$$ moves the graph to the right $$h$$ units.
 * Changing $$y$$ to $$y-k$$ moves the graph up $$k$$ units.
 * Changing $$x$$ to $$x/b$$ stretches the graph horizontally by a factor of $$b$$. (think of the $$x$$ as being dilated)
 * Changing $$y$$ to $$y/a$$ stretches the graph vertically.
 * Changing $$x$$ to $$x\cos A+ y\sin A$$ and changing $$y$$ to $$-x\sin A + y\cos A$$ rotates the graph by an angle $$A$$.

There are other standard transformation not typically studied in elementary analytic geometry because the transformations change the shape of objects in ways not usually considered. Skewing is an example of a transformation not usually considered. For more information, consult the Wikipedia article on affine transformations.

For example, the parent function $$y=1/x$$ has a horizontal and a vertical asymptote, and occupies the first and third quadrant, and all of its transformed forms have one horizontal and vertical asymptote, and occupies either the 1st and 3rd or 2nd and 4th quadrant. In general, if $$y=f(x)$$, then it can be transformed into $$y=af(b(x-k))+h$$. In the new transformed function, $$a$$ is the factor that vertically stretches the function if it is greater than 1 or vertically compresses the function if it is less than 1, and for negative $$a$$ values, the function is reflected in the $$x$$-axis. The $$b$$ value compresses the graph of the function horizontally if greater than 1 and stretches the function horizontally if less than 1, and like $$a$$, reflects the function in the $$y$$-axis when it is negative. The $$k$$ and $$h$$ values introduce translations, $$h$$, vertical, and $$k$$ horizontal. Positive $$h$$ and $$k$$ values mean the function is translated to the positive end of its axis and negative meaning translation towards the negative end.

Transformations can be applied to any geometric equation whether or not the equation represents a function. Transformations can be considered as individual transactions or in combinations.

Suppose that $$R(x,y)$$ is a relation in the $$xy$$ plane. For example, $$x^2+y^2-1=0$$ is the relation that describes the unit circle.

Finding intersections of geometric objects
For two geometric objects P and Q represented by the relations $$P(x,y)$$ and $$Q(x,y)$$ the intersection is the collection of all points $$(x,y)$$ which are in both relations.

For example, $$P$$ might be the circle with radius 1 and center $$(0,0)$$: $$P = \{(x,y) | x^2+y^2=1\}$$ and $$Q$$ might be the circle with radius 1 and center $$(1,0): Q = \{(x,y) | (x-1)^2+y^2=1\}$$. The intersection of these two circles is the collection of points which make both equations true. Does the point $$(0,0)$$ make both equations true? Using $$(0,0)$$ for $$(x,y)$$, the equation for $$Q$$ becomes $$(0-1)^2+0^2=1$$ or $$(-1)^2=1$$ which is true, so $$(0,0)$$ is in the relation $$Q$$. On the other hand, still using $$(0,0)$$ for $$(x,y)$$ the equation for $$P$$ becomes $$0^2+0^2=1$$ or $$0=1$$ which is false. $$(0,0)$$ is not in $$P$$ so it is not in the intersection.

The intersection of $$P$$ and $$Q$$ can be found by solving the simultaneous equations:

$$x^2+y^2 = 1$$ $$(x-1)^2+y^2 = 1.$$

Traditional methods for finding intersections include substitution and elimination.

Substitution: Solve the first equation for $$y$$ in terms of $$x$$ and then substitute the expression for $$y$$ into the second equation:

$$x^2+y^2 = 1$$ $$y^2=1-x^2.$$

We then substitute this value for $$y^2$$ into the other equation and proceed to solve for $$x$$: $$(x-1)^2+(1-x^2)=1$$ $$x^2 -2x +1 +1 -x^2 =1$$ $$-2x = -1$$ $$x=1/2.$$

Next, we place this value of $$x$$ in either of the original equations and solve for $$y$$:

$$(1/2)^2+y^2 = 1$$ $$y^2 =3/4$$ $$y = \frac{\pm \sqrt{3}}{2}.$$

So our intersection has two points: $$ \left(1/2,\frac{+ \sqrt{3}}{2}\right) \;\; \text{and} \;\;  \left(1/2,\frac{-\sqrt{3}}{2}\right). $$

Elimination: Add (or subtract) a multiple of one equation to the other equation so that one of the variables is eliminated. For our current example, if we subtract the first equation from the second we get $$(x-1)^2-x^2=0$$. The $$y^2$$ in the first equation is subtracted from the $$y^2$$ in the second equation leaving no $$y$$ term. The variable $$y$$ has been eliminated. We then solve the remaining equation for $$x$$, in the same way as in the substitution method:

$$x^2 -2x +1 -x^2 =0 $$ $$-2x = -1$$ $$x=1/2.$$

We then place this value of $$x$$ in either of the original equations and solve for $$y$$: $$(1/2)^2+y^2 = 1$$ $$y^2 = 3/4$$ $$y = \frac{\pm \sqrt{3}}{2}.$$

So our intersection has two points: $$ \left(1/2,\frac{+ \sqrt{3}}{2}\right) \;\; \text{and} \;\; \left(1/2,\frac{-\sqrt{3}}{2}\right). $$

For conic sections, as many as 4 points might be in the intersection.

Finding intercepts
One type of intersection which is widely studied is the intersection of a geometric object with the $$x$$ and $$y$$ coordinate axes.

The intersection of a geometric object and the $$y$$-axis is called the $$y$$-intercept of the object. The intersection of a geometric object and the $$x$$-axis is called the $$x$$-intercept of the object.

For the line $$y=mx+b$$, the parameter $$b$$ specifies the point where the line crosses the $$y$$ axis. Depending on the context, either $$b$$ or the point $$(0,b)$$ is called the $$y$$-intercept.

Geometric axis
Axis in geometry is the perpendicular line to any line, object or a surface.

Also for this may be used the common language use as a: normal (perpendicular) line, otherwise in engineering as axial line.

In geometry, a normal is an object such as a line or vector that is perpendicular to a given object. For example, in the two-dimensional case, the normal line to a curve at a given point is the line perpendicular to the tangent line to the curve at the point.

In the three-dimensional case a surface normal, or simply normal, to a surface at a point P is a vector that is perpendicular to the tangent plane to that surface at P. The word "normal" is also used as an adjective: a line normal to a plane, the normal component of a force, the normal vector, etc. The concept of normality generalizes to orthogonality.

Spherical and nonlinear planes and their tangents
Tangent is the linear approximation of a spherical or other curved or twisted line of a function.

Tangent lines and planes
In geometry, the tangent line (or simply tangent) to a plane curve at a given point is the straight line that "just touches" the curve at that point. Informally, it is a line through a pair of infinitely close points on the curve. More precisely, a straight line is said to be a tangent of a curve y = f(x) at a point x = c on the curve if the line passes through the point (c, f(c)) on the curve and has slope f'(c) where f' is the derivative of f. A similar definition applies to space curves and curves in n-dimensional Euclidean space.

As it passes through the point where the tangent line and the curve meet, called the point of tangency, the tangent line is "going in the same direction" as the curve, and is thus the best straight-line approximation to the curve at that point.

Similarly, the tangent plane to a surface at a given point is the plane that "just touches" the surface at that point. The concept of a tangent is one of the most fundamental notions in differential geometry and has been extensively generalized; see Tangent space.

Books

 * John Casey (1885) Analytic Geometry of the Point, Line, Circle, and Conic Sections, link from Internet Archive.
 * Mikhail Postnikov (1982) Lectures in Geometry Semester I Analytic Geometry via Internet Archive
 * John Casey (1885) Analytic Geometry of the Point, Line, Circle, and Conic Sections, link from Internet Archive.
 * Mikhail Postnikov (1982) Lectures in Geometry Semester I Analytic Geometry via Internet Archive
 * Mikhail Postnikov (1982) Lectures in Geometry Semester I Analytic Geometry via Internet Archive

title: Analytic geometry


text:
Arabic alphabet

The Arabic alphabet (الْأَبْجَدِيَّة الْعَرَبِيَّة,  or الْحُرُوف الْعَرَبِيَّة, ), or Arabic abjad, is the Arabic script as specifically codified for writing the Arabic language. It is written from right-to-left in a cursive style, and includes 28 letters, of which most have contextual letterforms. The Arabic alphabet is considered an abjad, with only consonants required to be written; due to its optional use of diacritics to notate vowels, it is considered an impure abjad.

Letters
The basic Arabic alphabet contains 28 letters. Forms using the Arabic script to write other languages added and removed letters: for example Persian, Ottoman Turkish, Kurdish, Urdu, Sindhi, Azerbaijani, Malay, Acehnese, Banjarese, Javanese, Pashto, Punjabi, Uyghur, Arwi and Arabi Malayalam all have additional letters in their alphabets. Unlike Greek-derived alphabets, Arabic has no distinct upper and lower case letterforms.

Many letters look similar but are distinguished from one another by dots above or below their central part. These dots are an integral part of a letter, since they distinguish between letters that represent different sounds. For example, the Arabic letters ب, ت , and ث have the same basic shape, but with one dot added below, two dots added above, and three dots added above respectively. The letter ن also has the same form in initial and medial forms, with one dot added above, though it is somewhat different in its isolated and final forms.

Both printed and written Arabic are cursive, with most letters within a word directly joined to adjacent letters.

Alphabetical order
There are two main collating sequences ('alphabetical orderings') for the Arabic alphabet:, and.

The original order derives from that used by the Phoenician alphabet, and is therefore reminiscent of the orderings of other alphabets, such as those in Hebrew and Greek. With this ordering, letters are also used as numbers known as abjad numerals, possessing the same numerological codes as in Hebrew gematria and Greek isopsephy.

The or  order is used when sorting lists of words and names, such as in phonebooks, classroom lists, and dictionaries. The ordering groups letters by the graphical similarity of the glyphs' shapes.

Abjadi
The order is not a simple correspondence with the earlier north Semitic alphabetic order, as it has a position corresponding to the Aramaic letter samek ס, which has no cognate letter in the Arabic alphabet historically.

The loss of was compensated for by:
 * In the Mashriqi abjad sequence, the letter shin ש was split into two Arabic letters, ش and ﺱ, the latter of which took the place of.
 * In the Maghrebi abjad sequence, the letter Tsade (letter) צ was split into two independent Arabic letters, ض and ص, with the latter taking the place of.

The six other letters that do not correspond to any north Semitic letter are placed at the end.

This is commonly vocalized as follows:

Another vocalization is:

This can be vocalized as:

Modern dictionaries and other reference books do not use the order to sort alphabetically; instead, the newer  order is used wherein letters are partially grouped together by similarity of shape. The order is never used as numerals.

In the order replaced recently  by the Mashriqi order,  though still used in many Quranic schools in Algeria, the sequence is:

In Abu Muhammad al-Hasan al-Hamdani's encyclopedia الإكليل من أخبار اليمن وأنساب حمير, the letter sequence is:

Letter forms
The Arabic alphabet is always cursive and letters vary in shape depending on their position within a word. Letters can exhibit up to four distinct forms corresponding to an initial, medial (middle), final, or isolated position (IMFI). While some letters show considerable variations, others remain almost identical across all four positions. Generally, letters in the same word are linked together on both sides by short horizontal lines, but six letters (و ,ز ,ر ,ذ ,د ,ا) can only be linked to their preceding letter. In addition, some letter combinations are written as ligatures (special shapes), notably لا, which is the only mandatory ligature (the unligated combination ل‍ا is considered difficult to read).

Table of basic letters
Notes

 * See the article Romanization of Arabic for details on various transliteration schemes. Arabic language speakers may usually not follow a standardized scheme when transcribing words or names. Some Arabic letters which do not have an equivalent in English (such as ط) are often spelled as numbers when Romanized. Also names are regularly transcribed as pronounced locally, not as pronounced in Literary Arabic (if they were of Arabic origin).
 * Regarding pronunciation, the phonemic values given are those of Modern Standard Arabic, which is taught in schools and universities. In practice, pronunciation may vary considerably from region to region. For more details concerning the pronunciation of Arabic, consult the articles Arabic phonology and varieties of Arabic.
 * The names of the Arabic letters can be thought of as abstractions of an older version where they were meaningful words in the Proto-Semitic language. Names of Arabic letters may have quite different names popularly.
 * Six letters (و ز ر ذ د ا) do not have a distinct medial form and have to be written with their final form without being connected to the next letter. Their initial form matches the isolated form. The following letter is written in its initial form, or isolated form if it is the final letter in the word.
 * The letter originated in the Phoenician alphabet as a consonant-sign indicating a glottal stop. Today it has lost its function as a consonant, and, together with  and, is a mater lectionis, a consonant sign standing in for a long vowel (see below), or as support for certain diacritics ( and ).
 * Arabic currently uses a punctuation mark called the (ء) to denote the glottal stop, written alone or with a carrier:
 * alone: ء
 * with a carrier: إ أ (above or under an ), ؤ (above a ), ئ (above a dotless or ).

 * In academic work, the hamzah is transliterated with the modifier letter right half ring (ʾ), while the modifier letter left half ring (ʿ) transliterates the letter Ayin (ع), which represents a different sound, not found in English.
 * The hamzah has a single form, since it is never linked to a preceding or following letter. However, it is sometimes combined with a, , or , and in that case the carrier behaves like an ordinary , , or , check the table below:

Hamzah forms
For the writing rule of each form, check Hamza.

Modified letters
The following are not individual letters, but rather different contextual variants of some of the Arabic letters.

Gemination
Gemination is the doubling of a consonant. Instead of writing the letter twice, Arabic places a W-shaped sign called, above it. Note that if a vowel occurs between the two consonants the letter will simply be written twice. The diacritic only appears where the consonant at the end of one syllable is identical to the initial consonant of the following syllable. (The generic term for such diacritical signs is ), e. g., درس (with full diacritics: دَرَسَ) is a Form I verb meaning to study, whereas درّس  (with full diacritics: دَرَّسَ) is the corresponding Form II verb, with the middle  consonant doubled, meaning to teach.

Nunation
Nunation (تنوين ) is the addition of a final  to a noun or adjective. The vowel before it indicates grammatical case. In written Arabic nunation is indicated by doubling the vowel diacritic at the end of the word.

Ligatures
The use of ligature in Arabic is common. There is one compulsory ligature, that for ل +  ا, which exists in two forms. All other ligatures, of which there are many, are optional.

A more complex ligature that combines as many as seven distinct components is commonly used to represent the word.

The only ligature within the primary range of Arabic script in Unicode (U+06xx) is +. This is the only one compulsory for fonts and word-processing. Other ranges are for compatibility to older standards and contain other ligatures, which are optional. Note: Unicode also has in its Presentation Form B FExx range a code for this ligature. If your browser and font are configured correctly for Arabic, the ligature displayed above should be identical to this one,  ARABIC LIGATURE LAM WITH ALEF ISOLATED FORM:

Note: Unicode also has in its Presentation Form B U+FExx range a code for this ligature. If your browser and font are configured correctly for Arabic, the ligature displayed above should be identical to this one:
 * ARABIC TATWEEL + +
 * ARABIC LIGATURE LAM WITH ALEF FINAL FORM

Another ligature in the Unicode Presentation Form A range U+FB50 to U+FDxx is the special code for glyph for the ligature ("God"),   ARABIC LIGATURE ALLAH ISOLATED FORM:

This is a work-around for the shortcomings of most text processors, which are incapable of displaying the correct vowel marks for the word in the Quran. Because Arabic script is used to write other texts rather than Quran only, rendering +  +  as the previous ligature is considered faulty.

If one of a number of the fonts (Noto Naskh Arabic, mry_KacstQurn, KacstOne, Nadeem, DejaVu Sans, Harmattan, Scheherazade, Lateef, Iranian Sans, Baghdad, DecoType Naskh) is installed on a computer (Iranian Sans is supported by Wikimedia web-fonts), the word will appear without diacritics.
 * + +  = LILLĀH (meaning "to Allāh [only to God]")
 * or  لله
 * + +  +  = ALLĀH (the Arabic word for "god")
 * or  الله
 * + +  +   ARABIC SHADDA +   ARABIC LETTER SUPERSCRIPT ALEF +
 *  اللّٰه (DejaVu Sans and KacstOne don't show the added superscript Alef)

An attempt to show them on the faulty fonts without automatically adding the gemination mark and the superscript alif, although may not display as desired on all browsers, is by adding the  (Zero width joiner) after the first or second
 * ( +) +  +   ZERO WIDTH JOINER +
 *

Vowels
Users of Arabic usually write long vowels but omit short ones, so readers must utilize their knowledge of the language in order to supply the missing vowels. However, in the education system and particularly in classes on Arabic grammar these vowels are used since they are crucial to the grammar. An Arabic sentence can have a completely different meaning by a subtle change of the vowels. This is why in an important text such as the the three basic vowel signs are mandated, like the Arabic diacritics and other types of marks, like the cantillation signs.

Short vowels
In the Arabic handwriting of everyday use, in general publications, and on street signs, short vowels are typically not written. On the other hand, copies of the cannot be endorsed by the religious institutes that review them unless the diacritics are included. Children's books, elementary school texts, and Arabic-language grammars in general will include diacritics to some degree. These are known as "vocalized" texts.

Short vowels may be written with diacritics placed above or below the consonant that precedes them in the syllable, called. All Arabic vowels, long and short, follow a consonant; in Arabic, words like "Ali" or "alif", for example, start with a consonant:,.

Long vowels
In the fully vocalized Arabic text found in texts such as the Quran, a long following a consonant other than a hamza is written with a short  sign  on the consonant plus an  after it; long  is written as a sign for short   plus a ; and long  as a sign for short   plus a. Briefly, = ;  = ; and  =. Long following a  may be represented by an  or by a free  followed by an  (two consecutive s are never allowed in Arabic).

The table below shows vowels placed above or below a dotted circle replacing a primary consonant letter or a Shadda sign. For clarity in the table, the primary letters on the left used to mark these long vowels are shown only in their isolated form. Most consonants do connect to the left with, and  written then with their medial or final form. Additionally, the letter in the last row may connect to the letter on its left, and then will use a medial or initial form. Use the table of primary letters to look at their actual glyph and joining types.

In unvocalized text (one in which the short vowels are not marked), the long vowels are represented by the vowel in question:, , or. Long vowels written in the middle of a word of unvocalized text are treated like consonants with a (see below) in a text that has full diacritics. Here also, the table shows long vowel letters only in isolated form for clarity.

Combinations وا and يا are always pronounced and  respectively. The exception is the suffix ـوا۟ in verb endings where is silent, resulting in  or.

In addition, when transliterating names and loanwords, Arabic language speakers write out most or all the vowels as long ( with ا, and  with ي , and  and  with و ), meaning it approaches a true alphabet.

Diphthongs
The diphthongs and  are represented in vocalized text as follows:

Vowel omission
An Arabic syllable can be open (ending with a vowel) or closed (ending with a consonant):
 * open: CV [consonant-vowel] (long or short vowel)
 * closed: CVC (short vowel only)

A normal text is composed only of a series of consonants plus vowel-lengthening letters; thus, the word qalb, "heart", is written qlb, and the word qalaba "he turned around", is also written qlb.

To write qalaba without this ambiguity, we could indicate that the l is followed by a short a by writing a fatḥah above it.

To write qalb, we would instead indicate that the l is followed by no vowel by marking it with a diacritic called sukūn, like this: قلْب.

This is one step down from full vocalization, where the vowel after the q would also be indicated by a fatḥah: قَلْب.

The Qurʾān is traditionally written in full vocalization.

The long i sound in some editions of the Qur’ān is written with a kasrah followed by a diacritic-less y, and long u by a ḍammah followed by a bare w. In others, these y and w carry a sukūn. Outside of the Qur’ān, the latter convention is extremely rare, to the point that y with sukūn will be unambiguously read as the diphthong, and w with sukūn will be read.

For example, the letters can be read like English meel or mail, or (theoretically) also like mayyal or mayil. But if a sukūn is added on the y then the m cannot have a sukūn (because two letters in a row cannot be sukūnated), cannot have a ḍammah (because there is never an uy sound in Arabic unless there is another vowel after the y), and cannot have a kasrah (because kasrah before sukūnated y is never found outside the Qur’ān), so it must have a fatḥah and the only possible pronunciation is (meaning mile, or even e-mail). By the same token, m-y-t with a sukūn over the y can be mayt but not mayyit or meet, and m-w-t with a sukūn on the w can only be mawt, not moot (iw is impossible when the w closes the syllable).

Vowel marks are always written as if the i‘rāb vowels were in fact pronounced, even when they must be skipped in actual pronunciation. So, when writing the name Aḥmad, it is optional to place a sukūn on the ḥ, but a sukūn is forbidden on the d, because it would carry a ḍammah if any other word followed, as in Aḥmadu zawjī "Ahmad is my husband".

Another example: the sentence that in correct literary Arabic must be pronounced Aḥmadu zawjun shirrīr "Ahmad is a wicked husband", is usually pronounced (due to influence from vernacular Arabic varieties) as Aḥmad zawj shirrīr. Yet, for the purposes of Arabic grammar and orthography, is treated as if it were not mispronounced and as if yet another word followed it, i.e., if adding any vowel marks, they must be added as if the pronunciation were Aḥmadu zawjun sharrīrun with a tanwīn 'un' at the end. So, it is correct to add an un tanwīn sign on the final r, but actually pronouncing it would be a hypercorrection. Also, it is never correct to write a sukūn on that r, even though in actual pronunciation it is (and in correct Arabic MUST be) sukūned.

Of course, if the correct i‘rāb is a sukūn, it may be optionally written.

ٰٰ The sukūn is also used for transliterating words into the Arabic script. The Persian word ماسک (mâsk, from the English word "mask"), for example, might be written with a sukūn above the ﺱ to signify that there is no vowel sound between that letter and the ک.

Regional variations
Some letters take a traditionally different form in specific regions:

The phoneme is considered native in most Arabic dialects, below are the different representations of the phoneme in native and loanwords:

Non-native letters to Standard Arabic
Some modified letters are used to represent non-native sounds of Modern Standard Arabic. These letters are used in transliterated names, loanwords and dialectal words.

 * 1)  is considered a native phoneme/allophone in some dialects, e.g. Kuwaiti and Iraqi dialects.
 * 2)  is considered a native phoneme (instead of ) in a number of  Levantine and North African dialects and as an allophone in others.
 * 3) The phoneme  is considered native in most Arabic dialects, but not always part of Modern Standard Arabic. E.g. in Egypt, ج spells  in all cases, the same applies to Oman, and coastal Yemen. Regionally, in MSA or dialects,  is differently spelled in loanwords; most commonly ج, غ, ق, and ك. For example, "golf" can be written جولف, غولف, قولف, or كولف.

Numerals
There are two main kinds of numerals used along with Arabic text; Western Arabic numerals and Eastern Arabic numerals. In most of present-day North Africa, the usual Western Arabic numerals are used. Like Western Arabic numerals, in Eastern Arabic numerals, the units are always right-most, and the highest value left-most. Eastern Arabic numbers are written from left to right.

Letters as numerals
In addition, the Arabic alphabet can be used to represent numbers (Abjad numerals). This usage is based on the order of the alphabet. أ is 1, ب  is 2, ج  is 3, and so on until ي  = 10, ك  = 20, ل  = 30, ..., ر  = 200, ..., غ  = 1000. This is sometimes used to produce chronograms.

History
The Arabic alphabet can be traced back to the Nabataean script used to write Nabataean Aramaic. The first known text in the Arabic alphabet is a late fourth-century inscription from 50 km east of  in Jordan, but the first dated one is a trilingual inscription at Zebed in Syria from 512. However, the epigraphic record is extremely sparse, with only five certainly pre-Islamic Arabic inscriptions surviving, though some others may be pre-Islamic. Later, dots were added above and below the letters to differentiate them. (The Aramaic language had fewer phonemes than the Arabic, and some originally distinct Aramaic letters had become indistinguishable in shape, so that in the early writings 14 distinct letter-shapes had to do duty for 28 sounds; cf. the similarly ambiguous Book Pahlavi.)

The first surviving document that definitely uses these dots is also the first surviving Arabic papyrus (PERF 558), dated April 643, although they did not become obligatory until much later. Important texts were and still are frequently memorized, especially in Qurʾan memorization.

Later still, vowel marks and the hamzah were introduced, beginning some time in the latter half of the 7th century, preceding the first invention of Syriac and Tiberian vocalizations. Initially, this was done by a system of red dots, said to have been commissioned in the Umayyad era by Abu al-Aswad al-Du'ali, a dot above =, a dot below = , a dot on the line = , and doubled dots indicated nunation. However, this was cumbersome and easily confusable with the letter-distinguishing dots, so about 100 years later, the modern system was adopted. The system was finalized around 786 by al-Khalil ibn Ahmad al-Farahidi.

Other tributes and alphabets written in Arabic dialects
Arabic dialects were written in different alphabets before the spread of the Arabic alphabet currently in use. The most important of these alphabets and inscriptions are the Safaitic inscriptions, amounting to 30,000 inscriptions discovered in the Levant desert.

There are about 3,700 inscriptions in Hismaic in central Jordan and northwest of the Arabian Peninsula, and Nabataean inscriptions, the most important of which are the Umm al-Jimal I inscription and the Numara inscription.

Arabic printing
Medieval Arabic blockprinting flourished from the 10th century until the 14th. It was devoted only to very small texts, usually for use in amulets.

In 1514, following Johannes Gutenberg's invention of the printing press in 1450, Gregorio de Gregorii, a Venetian, published an entire prayer-book in Arabic script; it was entitled Kitab Salat al-Sawa'i and was intended for eastern Christian communities. Between 1580 and 1586, type designer Robert Granjon designed Arabic typefaces for Cardinal Ferdinando de' Medici, and the Medici Oriental Press published many Christian prayer and scholarly Arabic texts in the late 16th century. Maronite monks at Maar Quzhay Monastery on Mount Lebanon published the first Arabic books to use movable type in the Middle East. The monks transliterated the Arabic language using Syriac script.

Although Napoleon generally receives credit for introducing the printing press to Egypt during his invasion of the country in 1798, and though he did indeed bring printing presses and Arabic presses to print the French occupation's official newspaper Al-Tanbiyyah "The Courier", printing in the Arabic language had started several centuries earlier. A goldsmith (like Gutenberg) designed and implemented an Arabic-script movable-type printing-press in the Middle East. The Lebanese Melkite monk Abdallah Zakher set up an Arabic printing press using movable type at the monastery of Saint John at the town of Dhour El Shuwayr in Mount Lebanon, the first homemade press in Lebanon using Arabic script. He personally cut the type molds and did the founding of the typeface. The first book came off his press in 1734; this press continued in use until 1899.

Computers
The Arabic alphabet can be encoded using several character sets, including ISO-8859-6, Windows-1256 and Unicode, latter thanks to the "Arabic segment", entries U+0600 to U+06FF. However, none of the sets indicates the form that each character should take in context. It is left to the rendering engine to select the proper glyph to display for each character.

Each letter has a position-independent encoding in Unicode, and the rendering software can infer the correct glyph form (initial, medial, final or isolated) from its joining context. That is the current recommendation. However, for compatibility with previous standards, the initial, medial, final and isolated forms can also be encoded separately.

Unicode
As of Unicode, the Arabic script is contained in the following blocks:
 * Arabic (0600–06FF, 256 characters)
 * Arabic Supplement (0750–077F, 48 characters)
 * Arabic Extended-A (08A0–08FF, 96 characters)
 * Arabic Extended-B (0870–089F, 41 characters)
 * Arabic Extended-C (10EC0–10EFF, 3 characters)
 * Arabic Presentation Forms-A (FB50–FDFF, 631 characters)
 * Arabic Presentation Forms-B (FE70–FEFF, 141 characters)
 * Rumi Numeral Symbols (10E60–10E7F, 31 characters)
 * Indic Siyaq Numbers (1EC70–1ECBF, 68 characters)
 * Ottoman Siyaq Numbers (1ED00–1ED4F, 61 characters)
 * Arabic Mathematical Alphabetic Symbols (1EE00—1EEFF, 143 characters)

The basic Arabic range encodes the standard letters and diacritics but does not encode contextual forms (U+0621-U+0652 being directly based on ISO 8859-6). It also includes the most common diacritics and Arabic-Indic digits. U+06D6 to U+06ED encode Qur'anic annotation signs such as "end of ayah" ۝ۖ and "start of rub el hizb" ۞. The Arabic supplement range encodes letter variants mostly used for writing African (non-Arabic) languages. The Arabic Extended-A range encodes additional Qur'anic annotations and letter variants used for various non-Arabic languages.

The Arabic Presentation Forms-A range encodes contextual forms and ligatures of letter variants needed for Persian, Urdu, Sindhi and Central Asian languages. The Arabic Presentation Forms-B range encodes spacing forms of Arabic diacritics, and more contextual letter forms. The Arabic Mathematical Alphabetical Symbols block encodes characters used in Arabic mathematical expressions.

See also the notes of the section on modified letters.

Keyboards

Keyboards designed for different nations have different layouts, so proficiency in one style of keyboard, such as Iraq's, does not transfer to proficiency in another, such as Saudi Arabia's. Differences can include the location of non-alphabetic characters.

All Arabic keyboards allow typing Roman characters, e.g., for the URL in a web browser. Thus, each Arabic keyboard has both Arabic and Roman characters marked on the keys. Usually, the Roman characters of an Arabic keyboard conform to the QWERTY layout, but in North Africa, where French is the most common language typed using the Roman characters, the Arabic keyboards are AZERTY.

To encode a particular written form of a character, there are extra code points provided in Unicode which can be used to express the exact written form desired. The range Arabic presentation forms A (U+FB50 to U+FDFF) contain ligatures while the range Arabic presentation forms B (U+FE70 to U+FEFF) contains the positional variants. These effects are better achieved in Unicode by using the zero-width joiner and zero-width non-joiner, as these presentation forms are deprecated in Unicode and should generally only be used within the internals of text-rendering software; when using Unicode as an intermediate form for conversion between character encodings; or for backwards compatibility with implementations that rely on the hard-coding of glyph forms.

Finally, the Unicode encoding of Arabic is in logical order, that is, the characters are entered, and stored in computer memory, in the order that they are written and pronounced without worrying about the direction in which they will be displayed on paper or on the screen. Again, it is left to the rendering engine to present the characters in the correct direction, using Unicode's bi-directional text features. In this regard, if the Arabic words on this page are written left to right, it is an indication that the Unicode rendering engine used to display them is out of date.

There are competing online tools, e.g. Yamli editor, which allow entry of Arabic letters without having Arabic support installed on a PC, and without knowledge of the layout of the Arabic keyboard.

Handwriting recognition
The first software program of its kind in the world that identifies Arabic handwriting in real time was developed by researchers at Ben-Gurion University (BGU).

The prototype enables the user to write Arabic words by hand on an electronic screen, which then analyzes the text and translates it into printed Arabic letters in a thousandth of a second. The error rate is less than three percent, according to Dr. Jihad El-Sana, from BGU's department of computer sciences, who developed the system along with master's degree student Fadi Biadsy.

title: Arabic alphabet