Скачать или смотреть A really nice equation involving the fractional part of a variable

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sure! one interesting equation involving the fractional part of a variable is the sawtooth wave function. the sawtooth wave is a periodic waveform that resembles the teeth of a saw blade. it is defined by the equation:

\[ sawtooth(x) = x - \lfloor x \rfloor \]

where \( x \) is the input variable and \( \lfloor x \rfloor \) is the floor function that gives the largest integer less than or equal to \( x \).

the sawtooth wave function takes any real number \( x \) and returns the fractional part of that number between 0 and 1. it produces a repeating pattern that increases linearly from 0 to 1 within each period.

here is a code example in python to implement the sawtooth wave function:



in this code example, we define the `sawtooth` function that calculates the sawtooth wave for a given input `x`. we then generate a range of `x` values from -5 to 5 and calculate the corresponding sawtooth wave values using the function. finally, we plot the sawtooth wave function using matplotlib.

you can run this code in a python environment to visualize the sawtooth wave function and explore its properties.

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