Isfahan is in the 50 Most Beautiful Cities in the World

The traveler  Mag introduce the 50 Most Beautiful Cities in the World and Isfahan is one of it.

Isfahan by Traveler

We seek beauty in many forms: through art and architecture; from water views and mountain highs; in its people and its history. This list circles the globe, finding the most beautiful cities in the world from Italy to Iran. Vote for your favorite cities in the 2016 Readers’ Choice Awards survey.

Once one of the largest cities in the world, Isfahan had such serious cosmopolitan clout in the 16th century that it inspired the phrase Isfahan nesf-e jahan, or “Isfahan is half the world.” Today, it’s is one of the country’s largest metropolises, and has wide, tree-lined boulevards, significant Islamic architecture, and hidden Persian gardens, all perfect for exploring.

cosmopolitan clout in the 16th century that it inspired the phrase Isfahan nesf-e jahan, or “Isfahan is half the world.” Today, it’s is one of the country’s largest metropolises, and has wide, tree-lined boulevards, significant Islamic architecture, and hidden Persian gardens, all perfect for exploring.

The post Photo: Foreign tourists visit isfahan historical zone appeared first on IRAN This Way.

“Rif Isfahan” team was second and “Organa Hormozgan” team was third.

Video: Iran women’s softball league final match 2022

Softball was started in Iran in 1997 with the help of Japanese living in Tehran, and today more than 250 female athletes are active in softball in more than 10 provinces.

The post Photo: Tehran is the champion of Iran women’s softball league appeared first on IRAN This Way.

The swiss FM first destination was Isfahan; land of culture & UNESCO world heritage sites. The reason why he travel to Iran is to mark the centenary of swiss-Iran diplomatic relations so he stayed one day and two nights in Isfahan, visited seven monuments (including mosques,cathedral,royal palaces,Persian garden,carvansaray changed to 5-star hotel,traditional house changed to a hotel and UNESCO world heritage square.

Ignazio Cassis tweet:“Visit to the city of Isfahan, a pearl in the Middle East. Knowing the culture and people of a country…”

Video Report: Nafiseh Hajati

Isfahan is in the 50 Most Beautiful Cities in the World

The traveler  Mag introduce the 50 Most Beautiful Cities in the World and Isfahan is one of it.

Isfahan by Traveler

We seek beauty in many forms: through art and architecture; from water views and mountain highs; in its people and its history. This list circles the globe, finding the most beautiful cities in the world from Italy to Iran. Vote for your favorite cities in the 2016 Readers’ Choice Awards survey.

Once one of the largest cities in the world, Isfahan had such serious cosmopolitan clout in the 16th century that it inspired the phrase Isfahan nesf-e jahan, or “Isfahan is half the world.” Today, it’s is one of the country’s largest metropolises, and has wide, tree-lined boulevards, significant Islamic architecture, and hidden Persian gardens, all perfect for exploring.

cosmopolitan clout in the 16th century that it inspired the phrase Isfahan nesf-e jahan, or “Isfahan is half the world.” Today, it’s is one of the country’s largest metropolises, and has wide, tree-lined boulevards, significant Islamic architecture, and hidden Persian gardens, all perfect for exploring.

The post Video| Swiss FM visited Isfahan appeared first on IRAN This Way.

With the commissioning of Diesel Treatment Unit and installing new equipment before the termination of the current year [to end March 20, 2021], 22 million liters of diesel will be produced in the refinery according to Euro-5 standard, he said.

Of total 22 million liters of diesel currently produced in the refinery, 2 million liters is produced according to the Euro standard.

Presently, 12 million liters of gasoline is daily produced in the refinery, observing Euro-5 standard rules and regulations, Ebrahimi stressed.

Elsewhere in his remarks, Ebrahimi pointed to the commitments of his company in tandem with the social responsibilities and added, “Esfahan Oil Refining Company has assisted Municipality of Isfahan and Isfahan University of Medical Sciences financially in the fight against coronavirus.”

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This guide is designed to inspire travel to Iran and give practical travel tips that are hard to find for a country so rarely visited, with the second half outlining the best ways to get to Iran using your points. Make sure to read The Essentials section at the end of this piece.

All of the following images were taken by the author and should not be reproduced without permission.

1. Meet the friendliest people in the world

Word is that Iranians are the amongst the most genuine and approachable people in the world. Is it true?

I had high expectations…and they were met. I would put Iranians in the same category as the Japanese and Americans for hospitality.

Never before in my travels had I ever been stopped on the street so many times (in a non-intrusive way) to be asked:

• Where are you from?
• What did you think of Iran before you came?
• What do you think of it now?

2. Visit the most beautiful city in the world

Big call? Probably. There are many beautiful cities in the world – Kyoto, Sydney, Paris – but Iran’s second-biggest city and main tourist drawcard Isfahan definitely deserves a spot up there.

Built on the River Zayandehrood, even with its dry desert climate it is teeming with green parks, plenty of shade on walks along the river, beautiful bridges, and historic mosques, churches and palaces. If you are going to visit one place in Iran, this is the place to go.

3. Watch the sunset over the dunes in the middle of the desert

Yazd is the gateway desert city of Iran, with day and overnight tours into the desert.

The only sound we heard whilst watching the suns rays descend over the flowing desert dunes was a light breeze carving sand into new dune formations. Truly breathtaking.

4. Eat till your heart’s content

Foodies will love Iran, with primary dishes being lamb, mutton, chicken, eggplant, lentils, cheese, yoghurt, rice, dates and pita bread. Vegetarians will be slightly more limited in choices, but it is not prohibitive.

Having said that, all breakfasts tend to be vegetarian, made up of feta cheese, tomatoes, cucumbers, pita bread, yoghurt and watermelon.

Foodies of all persuasions should be sure to visit the moderately-priced vegetarian restaurant in the Iranian Artists’ Forum in Honarmandan Park (also known as Artists’ Park). The second time we went back the waiter brought us an extra course for free and two university professors at a nearby table joined us for lunch.

5. Visit some of the least tourist-filled mosques in the world

Even during the peak travel month of May, it was hard to encounter many other tourists at the majestic mosques that Iran puts a lot of effort into keeping beautiful.

Of course, be respectful of prayer times, take off your shoes and remember that there are separate areas for men and women. Be sure to check the opening times of mosques on the internet or with your accommodation so as to not be caught out by them being closed.

Mosques in Isfahan are the most expensive to get into (around $8 each), but are also the most beautiful.

6. Visit the ceremonial capital of the Persian Empire

Persepolis (literally ‘The Persian City’) brought together the 28 nations of the Persian Empire (at its peak) for ceremonies and was known as the United Nations of the empire.

Located 90 minutes east of Shiraz, choose the more reasonably-priced accommodation options in Shiraz rather than stay near the UNESCO-protected site, but avoid the midday and afternoon heat by catching a private taxi out for the 8am opening. A tour guide is highly recommended and can be organized upon arrival at the site.

7. Transport options are cheap and relatively efficient

Most transport is by road, so if looking to save money, go by bus, but we found it funny/frustrating how many times people were moved around the bus by the bus driver to make sure that women and men were not seated together. This strict policy is more the work of the government rather than the considerably liberally-minded population.

If you have a bit more money, then another option is a private driver, which will be faster and more comfortable, but you will miss out on the local bus experience.

The 10-12 hour overnight Chinese-built train between Tehran and Shiraz is highly recommended at about $25 for a seat which converts into a bed in a four-person single-sex air-conditioned compartment. Bring your own food – disappointing food on the train.

The essentials

• Safety: apart from the state execution of a prominent Saudi figure triggering protests in Tehran earlier this year, there is a reason that we rarely hear of violence and terrorist attacks in Iran compared to much more dangerous Middle Eastern countries like Turkey, Israel and Egypt. I can honestly say that I felt safer and less on-edge in Iran than in some European capitals like London, Paris and Brussels, and petty theft is quite uncommon. Of course, please take into account official government warnings and check that your travel insurance will be valid in Iran.
• Best time to go: as you would expect from a country with climatic extremes, spring (March to May) and autumn (September to October) are the best times to visit. We went in mid-May and the weather was gloriously sunny and warm-to-hot, without being oppressive.
• Money: take all the cash you may need for the trip…and then some. International cards do not work at Iranian ATMs, so take clean, relatively new US dollars, euros or pounds (not that they are worth much at the moment) to exchange at moneychangers on the street. Be sure to ask your hotel for the going rate before venturing out to change. In May 2016, it was 1 USD = 34,000 rials and 1 EUR = 38-39,000 rials. You can also pay in USD or EUR at most establishments, with change given in rials. Note that most prices are in ‘tomans’, which is one zero less than the price in rial, e.g. 1 USD = 34,000 rials = 3,400 tomans.
• Visas: Australians and New Zealanders are eligible to receive a visa on arrival at the major airports in Iran, including Tehran, Isfahan and Shiraz. You must bring along a copy of your travel insurance which states the dates of coverage as well as clearly indicating it covers travel in Iran. You will be required to pay a visa fee of about €145; most EU nationals pay €75, but as Australia and NZ are allies of the US, that’s where the difference comes from. If you have dual citizenship, try to see which passport gives you a cheaper visa fee. You also need to have a confirmed hotel reservation or letter of invitation printed out, and they will call your hotel to make sure it is legitimate. You do not need hotel bookings for your whole trip, just the first night or two. Expect this process at the airport to take 1-2 hours. Most international flights arrive between midnight and 6am, which is highly inconvenient, but just breathe and be patient. As of this year, any traveller eligible for the ESTA visa waiver program for the US that has travelled to Iran in the past five years will need to apply for a tourist visa at their nearest US embassy or consulate when travelling to the US.
• Money and costs: Budget Your Trip estimates that in Iran you will spend about the same as what you would in Thailand or Mexico, half of what you would in Greece, or double what you would in India. Tehran is surprisingly pricey, especially for accommodation, but the real gems of Iran are outside the capital, so you shouldn’t be spending too much time there anyway. For basic private accommodation for two with breakfast included (always), intercity bus or train transport, mid-range restaurant meals and an attraction or two a day, we spent an average of $60 AUD/NZD per person per day over ten days.
• Drinking water: Water is surprisingly perfectly safe to drink from the tap and Iran has the widest network of public drinking fountains in streets, parks, bus stations, etc that I have seen anywhere in the world.

The post 7 Reasons to Travel to Iran appeared first on IRAN This Way.

Emphasizing the country enjoys full security to host tourists, Iran’s Tourism Minister Ali-Asghar Mounesan, invited tourists across the world to experience a unique journey to the land of history and civilization, especially during the spring.
In a statement released on Saturday, Mounesan said, “Nowadays, the world is even more involved in fast and surprising upheavals and ups and downs as a result of unprecedented progress in technology and industry. As such, the modern human is also influenced by urban, mechanical life and his soul needs some refinement and relief.

In such a situation, only travel and tourism can give us relief, joy, and sympathy and provide us with unforgettable experiences and memorable coexistence. In fact, tourism can be thought of as a familial or friendly gathering, the pivotal contents of which are kindness, cooperation, and synergy. In this chaotic era, tourists are like a delightful breeze endearing our souls and uniting all the people from around the world, regardless of their race, country, language, and beliefs.”

“With a deep and practical faith in this attitude, the Iranian government is trying its best to pave the way for incoming tourists and this is why there is a significant growth in tourism infrastructure in our country. In this regard, some incentive such as visa waiver, 90-day visa on arrival, standard residence services, attractive tourism routes and packages, and cheapest and most secure tours to Iran along with the last international tourism standards have enabled us to experience a 53% growth in our inbound tourism, winning the first place in the world in this regard. In addition, when it comes to the prices, Iran has the most competitive prices for tourism in the world and has emerged as a new phenomenon in the world of tourism, attracting the attention of many countries,” the statement added.
“Even if we disregard all that has been said, the unique tourist attractions of Iran are a good reason to have a journey to the land of history, civilization, and nature. With 24 UNESCO World Heritage Sites, 34,000 Nationally Registered Heritages and 600 active museums, Iran has a huge capacity to receive international tourists. In addition, high security, cheap tours, premium travel facilities, hospitable people, numerous historic and natural treasures, unique ecotourism facilities, diverse tourism packages (historic-cultural tourism, sport tourism, marine tourism, food tourism, medical tourism, etc.), interesting rituals, and diverse handicrafts and traditional arts provide enough reasons to visit Iran,” he said.

“The rich history and civilization of this land, the numerous and spectacular tourist attractions, four-season weather, and high cultural and ethnic diversity have made an invaluable treasure of Iran and put this country in the top 10 tourist destinations in terms of tourism, cultural and natural attractions. Astonishing mountains, breathtaking glaciers, beautiful volcanos, pristine forests, green foothills, delightful lakes, springs and waterfalls, picturesque beaches and wonderful islands, historical sites and distinct architecture, globally registered cities and villages, diverse and colorful handicrafts, delicious traditional cuisine and organic, healing drinks, etc. are only a small part of the beauties you can visit while staying in Iran.”
He noted, “With such advantages, each day the beautiful and safe cities of Iran are hosting thousands of tourists from different countries, having enjoyed the unique experience, most of whom decide to return and bring new fellow travelers with them.
Hereby I invite all the tourists from around the world to visit Iran during these last months of the Persian year, as well as the spring, and experience a distinct journey to the land of history and civilization. A country-size guesthouse is wholeheartedly ready to receive tourists from around the world.”

Following the Iranian missile strikes targeting US forces in Iraq, as well as the accidental downing of Ukrainian passenger jet near Tehran, several major airlines have rerouted or canceled flights in the region.

But some days later after these incidents, Qatar Airways, Emirates and several other regional airlines, including Kuwait Airways and Abu Dhabi-based Etihad Airways have continued using Iranian and Iraqi airspace.

KLM airline also made an announcement on Thursday that it would resume flights over the Iranian and Iraqi skies.

“KLM uses a security management system to analyze risks and thus determine safe flight paths. Substantiated by such analyses, it is once again safe to fly over Iran and Iraq,” the statement said.

Some travel agencies also announced that they would continue to make trips to Iran.

The incident came hours after Iran fired ballistic missiles at two American military bases in neighboring Iraq to respond to the US assassination of a senior Iranian military commander in the Arab country earlier this month.

Iran introduces tourism capacities in Madrid fair

Iranian tourism officials held a special session at the 40th International Tourism Fair in Madrid (FITUR) on Friday to introduce the country’s tourism attractions.

Iran’s Ambassador to Spain Hassan Ghashghavi, who was present at the meeting, referred to the remarkable capacities of the two countries for cooperation in the fields of tourism and handicrafts, voicing Iran’s readiness for promoting collaboration in those spheres.

Referring to the 50% growth in the number of Spanish tourists to Iran over the past year, Ghashghavi said that Iran is among the top ten countries in terms of tourism attractions diversity.

The envoy said the promotion of the tourism industry is high on the Iranian government’s agenda, noting that given the capabilities of Spain in this sector, the issue can serve as one of the areas of cooperation between Tehran and Madrid.

The meeting was also attended by two Spanish tourists who explained their experience of visiting Iran. The two hailed Iranians’ hospitality and the country’s high security despite the anti-Iran propaganda.

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The port of Bushehr is located in 28,58 N and 50, 50 E in the north end of a peninsula on the coast of the Persian Gulf. This peninsula is 14 Km long. The depth of water is near to 7m in the external anchorage leading to internal anchorage by the external channel 9200m in length and from the internal anchorage to Khor Soltani, Bushehr berth and then to Khor Booder by the internal channel 3900m in length. The channel is 140m in average width.
Climate in Bushehr Port

Climate in Bushehr Port
Bushehr port has got a semi-tropical climate with very hot and humid Summer and temperate Winter. The seasonal South Western winds blow on Bushehr sea from the beginning of June to the end of October but they rarely reach the harbor. The seasonal North Eastern winds blow on Bushehr sea and sometimes very strongly on the land from the end of December to the beginning of May.
The power of North Wind usually reaches to 6 in Beaufort scale, but it may rarely border on 8.
The average power of Wind in Winter is 4 in Beaufort scale
The temperature range during summer is +35 to +40 degrees centigrade, whereas it mat border on +2 degrees centigrade in Winter.
The humidity range during Winter is %40 to %80 and %30 to %99 in Summer.

TIDAL RANGE
The ebb and tide in Bushehr port is diurnal. The tidal range differs from 1 m to 1.6 m.
The highest tide may reach to 2 m and the lowest ebb may border on .7 m. The speed of water current in the internal channel and Khore Soltani may reach to 2-3 knots in ebb and flow conditions
The maximum height of the wave in the external anchorage is almost 1.5 m and .6 in the internal anchorage. Services

ROAD SERVICES

The port of Bushehr is connected to neighboring cities via 4 important routes:

• Bushehr – Khormooj – Kangan – Lengeh – Bandar Abbas extended 920 Km in length.
• Bushehr – Borazjan – Shiraz extended 290 Km in length.
• Bushehr – Borazjan – Yasooj – Isfahan.
• Bushehr – Genaveh – Deylam – Mahshahr – Abadan extended 690 Km in length.

It is worth mentioning that Bushehr – Borazjan route is a highway

AIRPORT

The port of Bushehr is one of the most accessible ports of the country to airport with only 5 Km distance. The international airport of Bushehr is provided with domestic flights to Tehran, Isfahan, Shiraz, Mashad, Kish, Kharg and international flights to Dubi and Jaddeh.

SHIP BUILDING FACTORIES

These factories, located near the port, are capable of repairing vessels of any kind up to 2500 tons onshore and building offshore constructs. Iran -Sadra Company has up to now built some huge oil platforms belonged to Southern Pars Area.

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IRNA/ Kazem Ghane

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Who is Omar Khayyam

Lived 1048 – 1131.

Omar Khayyam’s full name was Ghiyath al-Din Abu’l-Fath Umar ibn Ibrahim Al-Nisaburi al-Khayyami. Khayyam studied philosophy at Naishapur. He lived in a time that did not make life easy for learned men unless they had the support of a ruler at one of the many courts. However Khayyam was an outstanding mathematician and astronomer and he did write several works including Problems of Arithmetic, a book on music, and one on algebra before he was 25 years old.

In the year 1072 AD, Omar Khayyam documented the most accurate year length ever calculated – a figure still accurate enough for most purposes in the modern world. Khayyam was an astronomer, astrologer, physician, philosopher, and mathematician: he made outstanding contributions in algebra. His poetry is better known in the West than any other non-Western poet.

The man himself remains something of an enigma. Different biographers have documented him as a fun-loving, wine-drinking agnostic; a closet Zoroastrian; a Sufi Muslim; an orthodox Sunni Moslem; and a follower of Ancient Greek philosophy. All agree that he was an outstanding intellectual. Advertisements

Beginnings

Omar Khayyam was born on May 18, 1048 in the great trading city of Nishapur in northern Persia. Today the city is in Iran. Omar’s father was Ebrahim Khayyami, a wealthy physician. Omar’s mother’s name is not known. Some authors have written that Omar’s father earned a living making tents because Khayyami means tent-maker. However, although many English-speakers are named Smith, it does not mean their fathers spent their days hammering hot metal on an anvil.

Omar’s family were Muslims. His father seems to have been relaxed about religion, employing a mathematician by the name of Bahmanyar bin Marzban, a devotee of the ancient Persian religion of Zoroastrianism, to tutor Omar. Bahmanyar had been a student of the great physician, scientist, and philosopher Avicenna, and he gave Omar a thorough education in science, philosophy, and mathematics. Khawjah al-Anbari taught Omar astronomy, guiding him through Ptolemy’s Almagest.

In his early teens Omar worked in his father’s surgery learning about medicine.

Omar Khayyam celebrated his eighteenth birthday in 1066. In the same year, Halley’s comet appeared in the heavens, William the Conqueror’s Norman Army invaded England, and Omar’s father Ebrahim died. A few months after Ebrahim’s death, Omar’s tutor Bahmanyar also died.

It was the end of an era in Omar Khayyam’s life. It was time to put his family’s affairs in order and move on.

Samarkand

Omar Khayyam joined one of the regular caravans making a three month journey from Nishapur to the great city of Samarkand, which is now in Uzbekistan. Samarkand was a center of scholarship, and Khayyam arrived there probably in 1068, aged 20.

In Samarkand he made contact with his father’s old friend Abu Tahir, who was governor and chief judge of the city. Tahir, observing Khayyam’s extraordinary talent with numbers, gave him a job in his office. Soon Khayyam was given a job in the king’s treasury.

While living in Samarkand, Khayyam made a major advance in algebra.

Omar Khayyam’s Contributions to Science

Algebra

At high school we learn about equations of the form ax² + bx + c = 0; these are called quadratic equations. Cubic equations are of the form ax³ + bx² + cx + d = 0. Naturally, cubic equations are harder to solve than quadratics.

Khayyam conjectured correctly that it is not possible to solve cubic equations using the traditional Ancient Greek geometrical tools of straightedge and compass. Other methods are required.

At the age of 22, in 1070, Khayyam published one of his greatest works: Treatise on Demonstration of Problems of Algebra and Balancing. In it he showed that a cubic equation can have more than one solution. He also showed how the intersections of conic sections such as parabolas and circles can be utilized to yield geometric solutions of cubic equations. Archimedes had actually started work in this field over a thousand years earlier, when he considered the specific problem of finding the ratio of the volume of one part of a sphere to another. Khayyam considered the problem in a more general, methodical way.

In the language of modern mathematics, Khayyam’s solution to the equation x³ + a²x = b features a parabola of equation x² = ay, a circle with diameter b/a², and a vertical line through the intersection point. The solution is given by the distance on the x-axis between the origin and the (red) vertical line. Image by Pieter Kuiper.

Khayyam’s solutions avoided negative coefficients and negative roots because negative numbers were not acknowledged in Islamic mathematics. (Some cultures, however, had incorporated negative numbers into mathematics – for example Brahmagupta had introduced negative numbers into Indian mathematics 400 years earlier.)

Although Khayyam’s achievement was magnificent, he was personally disappointed that he needed to utilize geometry to solve cubic equations – he had hoped to discover an algorithm using only algebra.

Treatise on Demonstration of Problems of Algebra and Balancing established Khayyam as a mathematician of the first rank, and his reputation spread quickly throughout Persia.

Following Khayyam’s breakthrough there was little significant progress on cubic equations until 1535, when Niccolo Tartaglia found general solutions for all cubic equations.

Khayyam’s algebra was not the system of letters and signs we use today. His algebra was expressed in words. So, where today we write:

Solve for x:

x² + 6 = 5x

Khayyam wrote: What is the amount of a square so that when 6 dirhams are added to it, it becomes equal to five roots of that square?

Linking Algebra and Geometry

Algebra and Geometry were successfully linked by Pierre de Fermat and René Descartes in the 1600s, resulting in the modern x-y coordinate system.

Khayyam’s work with cubics had made him certain that algebra and geometry were linked, and he cited Euclid’s Elements to support the idea:

Whoever thinks algebra is a trick in obtaining unknowns has thought it in vain. No attention should be paid to the fact that algebra and geometry are different in appearance. Algebras are geometric facts which are proved by Propositions 5 and 6 of Book 2 of Euclid’s Elements.

Length of Year

In 1073, Khayyam received an invitation to the Persian city of Isfahan, capital of the Seljuk Empire, to prepare a calendar that would work in an orderly way and be accurate forever – this was an era in which year lengths were regularly changed.

Khayyam’s invitation came from the two most powerful men in the Seljuk Empire, of which Persia was part: these were Malik Shah, Sultan of the empire, and Nizam al-Mulk, his vizier.

Khayyam recruited other talented scientists to accompany him to Isfahan in 1074. There he was paid an extraordinarily high salary and enjoyed a privileged lifestyle. Malik Shah paid Khayyam to found an observatory with an initial aim of making observations of the heavens for 30 years, during which time Saturn, the most distant planet then known, would complete an orbit.

Ptolemy’s universe – the model accepted by Omar Khayyam.

During his time in Isfahan, Khayyam measured the length of a year – to be specific the tropical year length – with remarkable accuracy and precision.

Khayyam found that 1,029,983 days made 2,820 years. This gives a tropical year length of 365.2422 days to seven significant figures. Although it has become fashionable to quote more decimal places than this, Khayyam’s input of 1,029,983 days contains seven significant figures, so it is unreasonable to quote more than this number of significant figures in the calculated year length.

Today we know that the length of a tropical year actually changes by as much as 30 minutes from year to year. The average tropical year length quoted today is 365.242189 days, which to seven significant figures is 365.2422 days – exactly the figure Khayyam arrived at almost a thousand years ago. The length of a tropical year is also increasing very slightly as time passes, although not enough between Khayyam’s era and our own to be noticeable on a scale of seven significant figures.

Malik Shah introduced Khayyam’s new calendar in the Seljuk Empire on March 15, 1079. It was used until the 20th century.

The Parallel Postulate

The 13 books of Euclid’s Elements published in about 300 BC were probably the most influential books in the entire history of mathematics. The Elements had been built on five geometric postulates – in other words five things that were assumed to be true about geometry: for example, all right angles are equal to one another.

The fifth of Euclid’s five postulates was the parallel postulate. The parallel postulate proved to be a source of puzzlement, irritation, and joy for mathematicians for millennia. The joy was usually short-lived, belonging to mathematicians who thought they had proven the postulate only to be disappointed when an error was identified in their ‘proof.’

Euclid had considered a straight line crossing two other straight lines. He looked at the situation when the interior angles (shown in the image below) add to less than 180 degrees. In these circumstances, he said that the two straight lines will eventually meet on the side of the two angles that add to less than 180 degrees.

a. When each angle is 90 degrees, the lines are parallel.
b. If one or both of the angles is less than 90 degrees, the lines will meet.

Since the time Elements was first published, mathematicians had been trying to use Euclid’s first four postulates to prove the parallel postulate. They were doomed to fail. We now know that it is impossible to prove the parallel postulate using Euclid’s other postulates.

Omar Khayyam’s attempt was interesting. In his Explanations of the Difficulties in the Postulates in Euclid’s Elements he asks his readers to consider a straight line AB:

He asks his readers to consider two equal lines that are perpendicular to AB and sees three possible arrangements, which can produce four-sided figures:

He then refutes the possibility that angles C and/or D can be anything other than right-angles and in the image above only the central option is possible. So, he believes he has proven the parallel postulate. In fact, he has not done so, all he has done is stated it in a different way.

What is interesting to historians of mathematics is that in Khayyam’s ideas – shown roughly in the images above – they can see the first glimmers of non-Euclidean geometry.

Some Personal Details and the End

Full details of Khayyam’s personal life are not known. He is believed to have married and had at least one son and one daughter.

In 1092, Malik Shah and his vizier both died – the first probably by poisoning, the second by assassination. Khayyam went into hiding during the resulting power struggle. His survival depended on lying low. He had been Malik Shah’s personal physician and become his close personal friend – which had made him enemies – and Khayyam’s poetry suggests his behavior may not have been devoutly religious – and this had also made him enemies. Khayyam actually published no poetry in his lifetime. Some of his musings would potentially have endangered his life.

After the power struggle, it took about 20 years for Khayyam to be fully rehabilitated and for him to emerge again, at 64 years of age, in the company of powerful people. However, he refused to teach. One of his poems suggests why this might be: The secrets which my book of love has bred,
Cannot be told for fear of loss of head;
Since none is fit to learn, or cares to know,
Tis better all my thoughts remain unsaid.

Omar Khayyam died at the age of 83 in his hometown of Nishapur on December 4, 1131. He was buried in a tomb whose location he had chosen in an orchard where blossom would fall twice a year.

Khayyam’s poetry was popularized in the 1800s by Edward FitzGerald’s translations in the Rubaiyat of Omar Khayyam. Khayyam became so admired in the West that in 1963 the Shah of Iran had his grave exhumed and Khayyam’s remains moved to a huge purpose-built mausoleum in Nishapur where tourists could pay homage to the great poet.

We shall end with one of Khayyam’s most famous and evocative quatrains: A Book of Verses underneath the Bough,
A Jug of Wine, a Loaf of Bread—and Thou
Beside me singing in the Wilderness—
And Wilderness is Paradise enow.”

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