# Sherlock Holmes’ Most Difficult Math Problem: Bicycle Tracks

`*** The Latin root word “trac” means to pull, as in the word “tractor.” [Source]`
`Upon selecting a few random points from the rear tire’s tracks and drawing tangent lines in a particular direction that reached those of the front tire, all tangent lines had to be of equal length. That would show that the bicycle had taken the direction of the tangent lines. However, if the tangent lines were of unequal length, it would mean that the bicycle had taken a direction opposite of the tangent lines drawn from the rear tire to the front.`
`If someone were skilled enough to turn a bicycle in a perfect circle, then the bike would leave tracks of two perfect circles on the ground. But of course, the smaller of the two circles would undoubtedly belong to the rear tire. However, because the circle is perfectly symmetrical, it would be impossible to distinguish whether the bicycle was turning clockwise or counterclockwise.`
`*** When you apply this method in the real world, you may notice that the rear tire does not always precisely follow the tractrix. This is because bicycles do not always have the same wheelbase. There are many types of bicycles; some are for racing, and some are for leisure. That results in differences in the design of their frames.Designers usually emplace the front fork and axle on a bicycle with great care and precision regarding its angle. The slightest change in the design can result in apparent differences in the bicycle’s continuity and wheelbase when turning or leaning.Though simple mathematical models such as this one often omit such real-world factors and considerations, they still offer us greater insight into how such principles work`

Math Teacher. Content Curator. Soccer player. Maradona fan. Mostly write about the lectures I love to learn better. alikayaspor@gmail.com

## More from Ali

Math Teacher. Content Curator. Soccer player. Maradona fan. Mostly write about the lectures I love to learn better. alikayaspor@gmail.com

## Linear Algebra 3 | Inverse Matrix, Elimination Matrix, LU Factorization, and Permutation Matrix

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