# Can ants do trigonometry?

Was just reading in Clifford A. Pickover's "The Math Book" that ants of the Sahara desert can, after wandering in a non-linear path to find food, from there go directly back home without a line of sight between the two locations.

I don't see how one can arrive at the correct direction and distance to travel without not only keeping track of footsteps and angles turned along the way, but knowing the sines and cosines of such angles, the ability to multiply numbers together, and then in effect having a table of the inverse tangent function and square roots to calculate the return trip.

I should mention that the essay only seems interested in the fact that the ants can keep track of the distance they travel by counting their steps, since artificially lengthening and shortening their legs messes up the voyage back accordingly.

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PeroK
Homework Helper
Gold Member
2020 Award
In the same way that a child learns to catch a ball without solving kinematic equations, the ants can no doubt work out the way home without explicitly doing the maths you suggest.

How they do it is a good question. But, just because it could be done with trigonometry, doesn't imply that's how they do it.

snoopies622
opus
Gold Member
Read something similar about dogs and when they see a kid on a bike riding perpendicular to their line of sight, they beeline to a point on the street that they know the bike will be by the time they get there!

Ryan_m_b
Staff Emeritus
Ants retrace their step to the colony by following their own pheromone trail. When they double back (primarily after finding food) it reinforces the trail and encourages other ants to use it. Routes with food at the end emergently become stronger trails and end up being taken by a majority of foresters. Eventually the line will straighten out because the random actions of ants cutting corners will lead to a shorter path, with quicker turn around and thus a stronger trail.

On my phone so struggling to find a good video to demonstrate but this timelapse shows some of the process:

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jim mcnamara, Tosh5457, berkeman and 1 other person
How they do it is a good question.

I guess we won't know until we learn to speak ant! Amazing what life on earth can do.

jim mcnamara
Mentor
@snoopies622 - we do know - see @Ryan_m_b answer above. What is going on here:
1. if an ant is first to find some food, it does in fact retrace it's originally circuitous path back home. Period. This is how ants navigate. E O Wilson has written dozens of papers on this topic. See the video link above.
2. the original observer has no way to know if this ant was first to find or if hundreds of other previous ants had made the trip and our study ant came on the food at a unique angle, and said 'Oh wow, here is the best path back home. To heck with my own trail.' Because only then did he "sniff" out the strong pheromone trail.
Why? Humans cannot perceive ant pheromone trails with our inborn set of senses.

PS: ants cannot talk or do math, but the thread title anthropomorphizes, so I can too. It's more fun that way.

berkeman
Lord Jestocost
Gold Member
1. if an ant is first to find some food, it does in fact retrace it's originally circuitous path back home. Period.

That's just not the case with desert ants. Desert ants are outstanding navigators. After a tortuous foraging trip, desert ants return on straight homewards paths. The terminology regarding this capability is “path integration” which results in a homebound global vector. See, for example, chapter 1.2 in [PDF]The desert ant's celestial compass system - Humboldt-Universität zu ...

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