Space usage.

Traffic space is a scarce resource in urban environments. Increasing density of road users, combined with limited available infrastructure, forces us to optimize the efficiency of the use of space by means of transport. This paper presents a mathematical model that investigates the relationship between the number of wheels on bicycles and the amount of traffic space occupied, with the aim of minimizing this space. The reasoning leads to the conclusion that the optimal number of wheels is ultimately negative, which has interesting theoretical implications for the design of future means of transport.

Mathematical model

Let x represent the number of wheels on a bicycle, where x is an integer. The amount of occupied traffic space R(x) as a function of the number of wheels can be modeled as follows:

R(x) = k * x + c

whereby:

• k is a positive constant representing the space per wheel,
• c is the minimum space that a bicycle without wheels (the frame) takes up.

To minimize the total space, we differentiate with respect to x:

dR(x)/dx = k

Since k > 0, R(x) is a strictly increasing function of x. The absolute minimum of R(x) is thus reached for the smallest possible number of wheels. Mathematically, this would imply that the optimal number of wheels would be from x to minus infinity (x → -∞).

Interpretation

In practical terms, a negative number of wheels is physically impossible, but in a theoretical framework this finding suggests that the concept of a “bicycle” itself needs to be rethought. A negative number of wheels implies a situation where the vehicle has less physical presence than a frame without wheels, which is only possible if the vehicle itself becomes virtual or abstract, or fully integrated into the infrastructure (e.g. through magnetic fields or floating mechanisms).

Conclusion

The mathematical model shows that minimal space usage is theoretically achieved when the number of wheels is negative. Although this seems physically impossible, it points to a fundamental problem in the current approach to mobility: as long as bicycles have a physical footprint, they take up space. The concept of a bicycle without wheels — or with a negative physical impact — opens up new perspectives for mobility, such as floating vehicles, virtual bicycles or fully integrated transport systems. Minimizing traffic space therefore requires a redefinition of the concept of “bicycle” itself.