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New condition Re>Re_th_min=124 of linear (exponential) instability of theHagen-Poisseuille (HP) with respect to extremely small by magnitudeaxially-symmetric disturbances of the tangential component of the velocityfield is obtained. For this, disturbances must necessarily have quasi-periodiclongitude variability (not representable as a Fourier series or integral) alongthe pipe axis that complies with experimental data and differs from the usuallyconsidered idealized case of pure periodic disturbances for which HP flow isstable for arbitrary large Reynolds numbers Re. Obtained minimal thresholdReynolds number is related to the spatial structure of disturbances (having tworadial modes with non-commensurable longitudinal periods) in which irrationalvalue p=1.58 of the ratio of the two longitudinal periods is close to the valueof the "golden ratio" equal to 1.618.

New Linear Theory of Hydrodynamic Instability of the Hagen-Poiseuille Flow