it's reporting that kim met the chinese president xi jinping for about an hour and it's likely they discussed a possible second summit with donald trump. the latest round of talks between the afghan taliban and the united states have been called off the differences over including members of the afghan government so discussions are underway in islamabad tween representatives from kabul and the pakistani government the u.s. secretary of state might pompei it has made an unannounced visit to iraq the latest stop on his middle east or he's reassuring washington's allies about trump's plans withdraw troops from syria. sudan's president omar al bashir is set to address a pro-government rally in the capital khartoum trying to counter mass protests against his presidency the demonstrations have spread across sudan since mid december it began over the rising cost of food and fuel and government corruption president bashir is refusing to resign. though the headlines got more news here in algeria right after science in the golden age. the week began

with views of ninety day truce in the tip for tap the u.s. china trade all the world's largest supplier of liquefied natural gas is leaving the biggest oil cartel we bring you the stories to the shaping the economic world we live in counting the cost on al-jazeera. they've been so many great advances in science over the past hundred years everything from relativity and quantum mechanics to electronics computing and space travel but none of this progress would have been possible without the mathematics of songs and the development of algebra the term algebra can be traced back to the

arabic word algebra which has its roots in the manuscript written around eight twenty during the time i refer to was the golden age of science this was the period between the ninth from fourteenth centuries when scholars in the islamic world first applied the principles of mathematics to science and jamal could be a british professor of theoretical physics but born in baghdad i'm going to look at how the mathematical underpinnings of science apply today and trace their roots back to this golden age.

aviation is one of the most remarkable achievements of modern science and in order to be sure that the planes we've built stay in the sky we've needed to master the mathematics of flying. this is we come on the and be green who's a jet pilot and a mathematician. we are straight. and you have the mathematics background so you understand more the most the mathematics involved in aviation and flying absolutely it's it is a great way to be able to understand how to fly an airplane to understand the dynamics of what's actually going on in the aircraft because i can actually dig into the equations and understand the science behind it. the mathematics that i'm interested in is something called a quadratic equation a square equation the unknown quantity x. times itself that square lower equation please the essential basic core dry take

these fundamental to how much lift an airplane can generate how fast it needs to fly it is the basis of all aviation it's actually not as complicated as many people might think if we think about lifts and there were some various constants and then there's haul off road so it looks complicated with lots of symbols but if you bracket all this all it's saying is lifts is some number it's hard to square of the velocity very simply if you go twice as fast you will get four times as much lift. which is why aerobatic airplanes are powerful they need to fly fast to do those very crisp very precise loops. if you want for instance to roll the airplane and if you double the speed we will roll four times as fast so it's better.

when andy increases his speed to twice as fast because the lift depends on the square this times as much lift so he can roll the plane four times despite. our modern methods to solving mathematical problems like these involving quadratic equations go all the way back to the golden age in fact to the wonderfully titled book and kitab. which translate says the compendious book on calculation by completion and balancing it was written by the nineteenth century persian mathematician hard as me now he wasn't the first man to solve

quadratic equations they go all the way back to antiquity but he was certainly the first mathematician to provide the general method the technique the recipe for solving them what we would today called the algorithm a word derived from alcoholism is a latinized name algorithm it's he's also rightly regarded as being the father of the field of algebra even the term algebra comes from the word job or in the title of his book. what's most remarkable about this mathematical textbook though is not that it has any equations in it because it is me wrote his whole book in words alone. his muse book contains many practical everyday problems of the time such as dividing up land paying laborers splitting up inheritance businessmen and traders would have found the equations particularly helpful that's a very business man resort on a high tree grew up in the desert raising camels and still keeps

a herd today. so i mean these are beautiful camels thank you how important are camels in arabian and bedouin culture well come of a very important and bad when culture for transportation or milking for meat it's very important here and if i wanted to buy a camel i mean what sort of price would they fetch that expensive you know. fifty thousand to seven hundred million euros wow yes that beauty of the expansive talking about. millions you know that's not to say there's a jealous i guess they're both jealous yes there will be attention it's very very important i mean very expensive twenty million maybe more simple one is maybe five thousand two thousand i ask you this because i want to use the value of a camel to carry out a particular mathematical calculation while. i want to give you

a problem and show you the sort of thing the horrors me wrote about in his book of algebra going to use the example of a man who dies owning just one camel which of course has to be sold now what if that camel fetched eighty durham's the man has a friend to me bequeath a quarter of his money he leaves the widow to me because we've won eight and he has three sons how my. does each son get he would set up the algebraic equation where the unknown quantity the thing shape is part of the equation this is what we call x. in algebra today so the way i would write it is eighty equals eighty divided by four plus eighty divided by eight plus three x. three sons each receiving x. that's what we have to work out as we work through the algorithm the recipe to work this out so if

a simplify this eighty equals twenty plus ten plus three x. so eighties thirty plus three x. i take the thirty to the other side eighty minus thirty three x. fifty equals three x. and so x. is fifty over three which of i'm correct is sixteen and two third's there are times this sort of algebraic equation is something very complicated people at the time of horrors me showed the recipe for carrying out very important calculations that would have been used in everyday life. that's right isn't it.

andy green isn't just a pilot he's also a world record holder in one thousand nine hundred seven he became the first and only driver to officially travel on land faster than the speed of sound. is the longest standing record in history and up till this point nobody has broken it that's about to change with building a new car to go a lot faster. we are now building a bloodhound supersonic car it is going to be a car like no other. bloodhound has been designed using the latest engineering techniques and complex computer modeling to create such an advanced to be a cool bloodhound engineers have solved thousands of equations we're going to put the limits of modern technology one thousand six hundred kilometers an hour one thousand miles an hour forty percent faster than the speed of sound and when

traveling that fast some of the most important equations deal with drag the force of resistance that the car needs to overcome to reach a thousand six hundred kilometers an hour. exactly the same way that lift will increase by a factor of four when you double the speed the drag on the vehicle will also increase how much drag you will experience is again a square law and it's even more extreme in the land speed record context because of course we're going so much false about the square is so enormous we're looking at sixteen hundred kilometers an hour square that it becomes a very big number and the amount of drag is immense to call. eight such an advanced high speed vehicle as one is quadratics the bloodhound engineers have also needed to solve many other types of equations press it was the car is nice work on quadratic equations then inspired other later mathematicians to solve even more complicated equations and another great i am who is regarded as one of the greatest

medieval poets in my view was an even better mathematician he was solving cubic equations involving a quantity times itself heart itself again and this is also important for bloodhound because the amount of power that's needed from the engines is a cubic equation it's extraordinary that they make that step to the cubic equation they gave us the final building block because it's not only when we double the speed we have four times the drag but it takes eight on the power is that she added so you're trying to do and it becomes a very very large number it's that the tube which produces such a huge quantity fight they discovered it not able to answer his question.

it was just one of the many scholars who flourished in the ninth century although he was persian he spent his academic life in the city of baghdad which had become a renowned center of learning. during the first century after the birth of islam muslim armies conquered vast swathes of the old world they defeated the persians and entered iraq in seven sixty two the basset caves established their capital in the newly founded city of baghdad from which they roomed over their great empire for the next five centuries and it was in baghdad the established the famous battle hekmat house of wisdom now it's not known exactly where this was or even if it was a single academy but we do know that baghdad quickly became the greatest center of

knowledge of the medieval world there bastard rulers were generous patrons promoting knowledge and scholarship at the same money a library to stamboul i'm meeting professor. he studied the origins of the house of wisdom there are three. hundred to a long. he. flew below. the lake that. cost will her liver. be overturned. through the. method that. there was a rations they were christians they were jewish scholars or those under the auspices of the islamic empire being translated into arabic many of these scholars came from all sorts of religions all working together in this one big movement.

translation was central to the early work of the house of wisdom dr peter starr has studied this translation movements extensively. i think the translations are very central to the flourishing of sciences in islam one finds that the entire corpus of scientific literature finds its way into arabic so they were translating essentially from greek mainly from greek but also the languages are important as well from persian. from sun script when did this start so the end of the eighth century we find the translations really picking up that this is the bastard yes he's above all be a bastard period the earliest translations tend to be in those subjects which will serve the empire most medicine strong to me philosophy mathematics so without this remarkable translation movement that went on for two centuries there wouldn't have

been a golden age at all i think puts a very well. the house of wisdom was much more than just a library or translation house this was the high point of islamic civilization an unrivaled center of stuff. learning drawing on greek persian and indian texts the scholars there amassed a collection of world knowledge and then built on it through their own discoveries . the significance example of this use and development of knowledge from other civilizations was in geometry. slamming decoration is famous for its intricate patterns and geometric designs

developed over the centuries very often these were derived from earlier cultures greek roman by zentai persian and central asia they took that knowledge and created from it these beautiful patterns. geometry wasn't just about beauty of heart as me and other scholars from the house of wisdom translated books about mathematics and geometry in order to apply that knowledge to their world to their very practical reasons for studying geometry. the arabs have now an enormous empire need to measure it into taxing the book of elements of euclid euclid's elements with your suzumiya barriers some to last you're. building on the translations they studied the scholars of battle heckman improved upon the measurements of the greeks enabling them to create more accurate maps of the world. their mastery of geometry also allowed the scholars to make

astronomical calculations and describe the movements of the moon planets and stars . as a merchant one of the most fundamental aspects of mathematics was simply how to write numbers down in the golden age there were several systems in use including using arabic letters for numbers similar to roman numerals. advocated a different number system. the number system we used today the decimal system is called the hindu arabic numeral system called hindu because it comes a originally from india arabic because it came by the islamic world and scholars in baghdad like me transmitted it first. and then to the rest of the world everywhere today we use this decimal system one to nine and the zero and we forget how

difficult it was before it existed. so imagine if i wanted to add up my bill but not using the decimal system using roman numerals instead let's see how awkward that would be if i first write these numbers down using hindu arabic numerals forty two sixteen and fourteen now i can add these up very easily the sixteen forty makes thirty plus the forty two is seventy two. in roman numerals forty two would be x l r. sixteen is x v. fourteen is x v. i have to break this down now how many x. is forty so that actually four x. is. and then. and then i have another x. we are. going to have an. and for.

ok so now i have six x. x. x. x. . then i have a v. . and then i have one two three four seven so that's not a v. . they give me another x. so finally one two three four five six seven that. which is seventy two so i've got the right number but it took a lot longer to calculate. in the late twelfth century the italian mathematician fibonacci travelled the world and came across these numbers in the islamic empire in twelve zero two he wrote his book lieber abaci the book of calculation in which he promoted the use of hindu

arabic numeral system over the roman numerals describing its many benefits for both merchants and mathematicians alike. uptake of the system was slow both in the islamic world and in europe in florence in twelve ninety nine they banned these new rules on the pretext that they were easier to falsify than roman numerals however common sense eventually prevailed and the new rule system was adopted throughout europe in the fifteenth century six hundred years after it was introduced to the islamic world. one of the most important fields of modern mathematics is computer encryption from email confidentiality to government security encryption plays a big role in an increasingly online digital world. and the study of encryption goes all the way back to the ninth century and the work of another famous mathematician from beta hickman. this is

a very interesting book i'm trying to figure out exactly what it's telling us it's a book by al-kindi the philosophy of the arabs now kindi was a great polymath he was a philosopher he was a mathematician he was a musician and i think the part here he talks about he's got a disk with the arabic alphabet and he talks about hunting the number a particular symbol appears kindi figures are the idea of frequency analysis that when a letter appears a certain number of times it's more common than other letters you can work out what it is can these text is the earliest known description of frequency analysis but that text was only discovered in one thousand nine hundred eighty seven before that we had no idea that this supposedly modern technique for studying cryptic messages was in use over a thousand years ago now one of the oldest and most simplest ways to encrypt

a message to make it secret is simply by substituting each letter by a different one let me show you. imagine we have a simple sentence al-kindi was a famous scholar now provided we have the key. key which is also called the cipher which by the way comes from the arabic word which means zero with i represent each letter with a different one so by looking at the table i would see that a corresponds to l. and l. corresponds to k. . kafer kindi k. corresponds to v. and so on in this way i can turn this sentence into something that's not readable unless you have the cipher. what if we have a paragraph like this which looks completely but. without the key without the cipher i can't work it out now if you don't have the cipher you can use frequency

analysis to try and figure out the meaning i know that the five most common letters in english language are e c i o n r so far as replace these into that text i can start to see patterns emerging for instance if i look at the most frequently occurring letter in the text is w. so i'm guessing w. is most likely. and i carry on like this until i start to recognise individual words so for instance a three letter word that begins with t. in with is most likely that gives me the code for the letter h. and so on. if. the.

developments in mathematics were the only legacy of the golden age the translation movement had introduced scholars to a wide range of subjects and they made advances in fields as diverse as astronomy and medicine they took the mathematics they developed and applied it to things chemistry and engineering science was now no longer just a philosophical pursuit the math matteis zation of science pave the way to a multitude of scientific advances. next time we look at state of the art robotic engineering you can see it moves like a robot work a very human fluid but discovered that the idea of automatic machines goes back over a thousand years. that's why it's us that in a sense this is an early programmable fears right much so that. we find out about complex mechanisms such as clocks musical instruments and water pumps as the more

to lose the water wheel round that's moving back because of forces like that that will piston. and investigate without a possible for knox could fly all the way back in the ninth century. in the next episode of science in a golden age i'll be exploring the contributions made by scholars during the medieval period in the field of engineering. the heights of sophistication in mechanics at the time was the extravagance. written around age fifty eighteen the book contains a range of ingenious inventions and contraptions. with. business updates brought to you by qatar airways going places together.

business updates brought to you by qatar airways going places together culturally i believe the muslims had a far greater affects all europe than europe hot on the middle east. the crusaders

fault for all should fall because that failed to recognize the moment. not holocaust it was in the the list of colonization that exploded religion in the name of the cross from the crusades an arab perspective to find a liberation at this time on a. this is al jazeera. this is the news hour live from doha coming up in the next sixty minutes and thousands more lives will be lost if we don't act right now president has appealed to fear not fact.