Flying mathematicians

Christina Sng for Maths@Singapore

Birds navigate flight with ease, while pilots require a radar, maps, computers, radio beacons, and navigation signals from GPS satellites to make the same journey. 

How do birds accomplish this? 

Keith Devlin, Dean of Science at Saint Mary’s College of California and Senior Researcher at Stanford University suggests that they use a combination of different methods:

1. Solar Navigation: Many birds use the sun to navigate. This means they need to know where the sun is in the sky at each moment of the migration. This requires the mastery of trigonometry. 

2. Magnetic Fields: Homing pigeons find their way home by following the magnetic field lines of the earth with the magnetic compass in their heads , a detail proven by scientists attaching small magnets to the heads of homing pigeons. 

These magnets deflect the Earth’s magnetic field around the birds, says Devlin, and cause them to fly off course in the same degree of deflection. This too, requires trigonometry.

3. Star Navigation: Indigo Buntings rely on the stars to navigate at night. In fact, they learn to recognize the pattern of stars in the night sky when they are still in the nest. 

Scientists discovered that nestling Indigo Buntings in the northern hemisphere watch the stars in the night sky wheel around Polaris above Earth’s north pole. They notice which star the others rotated around. 

As with solar navigation and magnetic field navigation, trigonometry is needed.

4. Polarized light. Devlin suggests that another possibility is birds discern polarization patterns in sunlight. 

He explains, “As the sun’s rays pass though our atmosphere, tiny molecules of air allow light waves traveling in certain directions to pass through,” while they absorb others. “The resulting polarized light forms an image like a large bow-tie  located overhead at sunset  pointing north and south.”

“Some birds can detect the polarization, and use it like a large compass in the sky…polarized light allows a bird to calibrate its compass. Determining the direction in which to fly requires…mathematics.”

For more, visit https://www.maa.org/external_archive/devlin/devlin_10_99.html

Thanks to Julia Craice @jcraice for making this photo available freely on Unsplash 

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