How a muslim scholar measured the radius of the Earth

          Ever wondered how was the size of the Earth measured? Well, here's a way how.
          I was quite amazed by the this documentary film entitled "Islam and Science" (part 2) released by BBC especially when Prof. Jim Al-khalili explained how a muslim scholar measured the radius of the Earth. Prof Al-khalili is a physics professor of University of Surrey. This film really suites him for he understands and can speak the Arabic language and it was advantageous for him because he had to delve into Muslim history and Arabic books.

          We, muslims, are required to face a direction towards Kaaba whenever we pray. And that leaves no excuse to anyone far from Kaaba. Wherever country a muslim resides, he should always find that direction. And this eventually led to the measuring of the Earth's radius.

Professor Al-khalili explained:

  "... A more reliable and sophisticated method for estimating the Earth's size was needed, and two centuries after Al-Ma'mun died, it came. What made it possible was a great leap of imagination. And the fact that, by 900 AD, much of the world's mathematical knowledge had been translated into Arabic, so scholars could scrutinize and improve on it. 

  Out of this obsession with scholarly learning came a true mathematical visionary - Abu Rayhan Muhammad Ibn Ahmad Al-Biruni. And like all Islamic scholars of the time, Al-Biruni was obsessed with the science and mathematics of the ancient Greeks, Babylonians and Indians. And because of the success of the Translation Movement, he had literally on his desk the great work on geometry by Euclid, Ptolemy's Almagest, the Indian text the Sindhind, and the famous work on algebra by Al-Khwarizmi."

Let me dissect this subject a little bit further. The way I see it, we need three things here:
1. astrolabe (this is just like a large protractor)
2. distance measuring device (in our present time, we can use the rolling Measuring wheel), and
3. knowledge on basic trigonometry.

So let’s try to follow what Birani did in measuring the radius of the Earth. Here we’ll use the most basic ideas in trigonometry. Okey, here we go. Find a fairly high mountain in which we can see the vast flat horizon, the sea. What I can never forget in this is that with few simple measurements around this mountain, you can measure the size of our whole world.

Here's the step made by Biruni.
Height of the mountain

1. Al Biruni’s first step was to work out the height of the mountain. He did this by going to two points at sea level and knowing the distance apart and them measuring the angles from these points to the mountain top. The two points and the mountain top must line in one straight line. In measuring the angle, he had to use an   Astrolabe.

Prof. Jim Al-khalili using the astrolabe in measuring the angle of inclination of the mountain top.

Angle of inclination from the two points are measured and the distance between them is denoted by d in this figure.

2. We may consider first the triangle on the right side (drawn by yellow lines). We may use the Sine Law to solve for the slanted side l.

3. Then, we consider the right triangle on the left. We can use the sine function to solve for the height h of the mountain. (Refer to the diagram above, the right triangle whose hypotenuse is the side l.)

Now, one more measurement is needed to get the size of the Earth.

Radius of the Earth

4. To get the last measurement, one must climb to the top of the mountain to measure the angle of the line of sight to the horizon as it dips below the horizontal.

As you can see from the diagram, the line connecting the mountain top and the point where the line of sight reaches the horizon is perpendicular to the line connecting center of the Earth and the the point where the line of sight reaches the horizon. And the distance between the center of the Earth and the mountain top is equal to the sum of the radius of the Earth and and the height of the mountain (h+R).

5. We now have a very huge right triangle where the hypotenuse is equal to the sum of the radius of the Earth and and the height of the mountain. 

and by using the identity

would eventually lead to the expression:

The accuracy of this measurement is remarkable achievement for someone 1000 years ago!

EXERCISE

If you wanna try the steps described above, here's a list of values.

The distance (d) between two points is 100 m. The angle of inclination from one point near the seashore is 24.5 degrees while the angle of inclination from the point nearer to the mountain is 26.5 degrees. From these three given values, you can calculate the height of the mountain.

The angle of declination is 0.5 degrees as measured when one is on the mountain top.

(These values were measured by Prof. Al-khalili. And following the steps described above obtains a value of the radius of the Earth far greater than the known value. Big error isn't it? Well, Prof. Al-khalili did the measurements only once. But the measurement of Al-Biruni was more accurate than this because he did it again and again.

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Why pigs are forbidden

The morning breeze was very cool... It was hitting every spot of my face. The street was so silent with very few people walking around. Sun was just about to rise. The time's so refreshing. I could have been walking very slowly in the street as I was also wondering what I might get from this short visit. When I reached the gate, I could see my classmates were already there, seated and waiting to hear words from master. I greeted them with Salam and I helped myself to reach a vacant spot to sit behind one of them. Soon, the master came out from the door, entered the sala, and sat comfortably in front of us.
"Do you know why we are not allowed to eat pigs?" He started with inquisitive eyes.
No-one dared to answer the question. Silence fell for a moment. As ordinary young muslims, we just knew that pigs were forbidden.
"Today I shall tell you one of the reasons why." said he. Then he paused, took a sip from his cup of tea.
"It was during the time of Prophet Noah (alayhissalam). The flood was already covering their land and destroyed their homes along with the disbelievers. Noah and his followers were safely boarded then in the Ark, the great ship. This ship was three storeys. The first level was for the land animals. The second accomodated the birds. And the third was for the human beings, Noah (alayhissalam) and his followers."
He paused for a while and took another sip of tea from his cup again.
"But there was no pig yet at that time... I should tell you." he said with a smile, glad at the growing curiosity in us. Some of us were surprised at that point. We were wondering then what was the connection of pig and the story of the flood.
"Days went by and the animals, satisfying their biological bodies, needed to eat their foods... And every intake of food would eventually require an extraction of dirt. And there were several kinds of animals present in that ship, all of them had to eat their foods and then defecate."
It was really a problem, I thought. With those animals, from every kind doing that, it'd be really a problem.
"Soon the bad smell in the ship became very awful." He continued with a smile. "Eventually, Noah (alayhissalam) prayed to God to help him in this predicament."
"And God answered his dutiful servant... 'Tap the belly of the elephant.' was the answer to Noah (alayhissalam). Then, by His command, he tapped the belly of the elephant. And the first pig came into being. And the pig started to eat all the impurities of the animals hence cleaning the ship and removed the awful smell from the ship.
"Islam advises all to eat clean and healthy foods. For if dirty foods are taken, diseases may arise or worse, wa naujubillah, the heart becomes dirty also (attitude of the one who eats becomes animalistic)."
May we always have a close watch at the foods we eat that we may always have a healthy body and a "humanly" attitude. Read More

Muslim Women attends national Physics conference

        This year’s Samahang Pisika ng Visayas at Mindanao (SPVM) was held at Andres Bonifacio College in Dipolog City. The annual event, now on its 13th, was a three-days activity that educate, update and allow interactions between physicists from all over the Philippines. This conference was held from October 20-22, 2011.

       Among the participants (more than 1600), there were three female Muslims. Their outfits were so distinct from the crowd. Just like any other “practicing Islam” women, they were beautifully covered from head to toe. They are the following.

1. Shalima Arriola, a Physicist from Basilan. She got her BS Physics degree from Western Mindanao State University, Zamboanga City and she is now working at Basilan State College, in Isabella City, Basilan.

2. Fareedah Matanog. A high school Physics teacher. She finished her BS Metallurgical Engineering in 1996 at Mindanao State University – Iligan Institute of Technology (MSU-IIT). She is presently working at Datu Calaca High School, in Marantao, Lanao Del Sur.

3. Ameera Jose. She is a BS Physics student at Western Mindanao State University, Zamboanga City. She is one of the authors of the scientific paper entitled “Aviation’s worst nightmare: microburst” published nationally by October 2011.

          History has it that, precisely in 8th to the end of the 13th century, Islam had patronized and fostered the Greek scientific heritage in the field of medicine, astronomy,mathematics, physics, chemistry and philosophy. Islam continued to add new scientific achievements which bear witness that Muslim were deeply and seriously interested in scientific research. It was on the cream of the Islamic scientific achievement of Andalusia that the European Renaissance and its modern scientific inventions were based.

       These three brave women are among the very few Muslims in the field of Physics here in Philippines, who serve as catalysts to motivate us and the future generation to lead the "revival" of scholastic attitude and scientific advancement in this modern age among muslims.

        To these sisters, More power to all of you!

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