Density of data points around a point in a k-dimensinoal spa

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I am looking for a way of calculating how close data points are to a specified point in a k-dimensional space. My current method involves pythag to calulate the distance between the specified point and each of the data points. However, when working with an order of 10,000 data points this is very computationally intensive and is too slow for my program. Does anyone have suggestions for an alternative algorithm to use to determine a point's proximity to other data?

Thanks in advance!