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It seems like a simple question: How big is the Earth?

Using modern scientific apparatus, we can now accurately measure the dimensions of our planet.

But hundreds of years ago, one man came very close, using just a mountain and some very clever geometry.

In ancient times, philosophers deduced that the world was round because, during a lunar eclipse, the Earth projected a circular shadow on the moon.

It was later suggested that rather than being a flat disk like a pizza, the Earth was in fact spherical, like a soccer ball.

The first near-accurate measurement of the Earth's circumference was calculated by a Persian scholar called Abū Rayḥān al-Bīrūnī.

**Abū Rayḥān al-Bīrūnī, ****11th Century**

He would calculate Earth's circumference using trigonometry: the relationship between the sides and angles of triangles.

**Trigonometry**

At sea level, Bīrūnī used a device called an astrolabe to measure the angle between the ground and the top of a mountain.

He then moved to a different location, along a straight line, and took another measurement.

Using trigonometry, Bīrūnī could use the distance between these points, and the angles they made with the peak, to calculate the height of the mountain.

Bīrūnī then climbed to the peak, and used the astrolabe to measure the angle to the horizon.

Then came the ingenious part.

Bīrūnī imagined a huge right triangle, joining the mountaintop, the horizon and the center of the Earth.

Bīrūnī knew the Earth was spherical. Trigonometry told him the angle to the horizon and the height of mountain could be used to calculate the radius of the Earth.

**Radius of a circle:**

Line from center to circumference

Bīrūnī knew that doubling the radius would give the diameter.

**Diameter of a circle:**

Line passing through center of circle

**Connects two points on circumference**

And he could now calculate the Earth's circumference using the formula π x d.

He deduced that the Earth's equator was approximately 40,000km round.

We now know that this was correct to an accuracy of more than 99%.

**Earth's circumference = 40,008 km**

Bīrūnī's extraordinary discovery shows that simple mathematics can be all you need to answer the biggest questions.