Consecutive integers in the recursive number sequences, the Fibonacci sequence (F n ) and the Lucas sequence (L n ), are detected in the lengths of solar-activity variations from ≈ 1 yr to ≈ 12 yr, measured in rigid rotations of the Sun at the helioseismologically determined frequency in the radiative zone, 433 ± 3 $433 \pm 3$ nHz. One rotation is denoted by the symbol Ω $\Omega $ . Firstly, in the new international sunspot-number record (Ri) the most frequent (modal) sunspot-cycle length, which is also the period defined by autocorrelation for the recurrence of sunspot cycles, has been 144 ± ≈ 2 Ω $144 \pm \approx 2~\Omega $ ( F 12 = 144 $\mbox{F}_{12} = 144$ ). The most frequent length for a descending leg of the cycle has been 89 ± 2 Ω $\Omega $ (F = 11 89 $_{11} = 89$ ), and for an ascending leg 55 ± 1 Ω $\Omega $ (F = 10 55 $_{10} = 55$ ). Secondly, there is some observational evidence of Ri spectral peaks at the consecutive L n numbers of Ω $\Omega $ : 18 Ω $\Omega $ (≈ 1.3 yr), 29 Ω $\Omega $ (≈ 2.1 yr), 47 Ω $\Omega $ (≈ 3.4 yr), and 76 Ω $\Omega $ (≈ 5.6 yr), which are harmonics of the 144 Ω $\Omega $ period divided by the first four F > n 1 $_{{n}} > 1$ : 2, 3, 5, and 8. The numbers of Ω $\Omega $ : 144, 89, and 55 may be kinematical thresholds in the dynamo process starting at sunspot maximum, when the poles change polarity and the process is re-set. The ratio of two consecutive F n or L n converges to 1 + 5 2 $\frac{1+ \sqrt{5}}{2}$ , hence it is suggested that this proportion plays a role in solar behavior over time , described numerically. The length ratio 1 + 5 2 $\frac{1+ \sqrt{5}}{2}$ also is characteristic of fivefold symmetry in space . Since the icosahedral group is the link between numerical and spatial expressions of fivefold symmetry, it is proposed that the presence of icosahedral symmetry in the large-scale geometry of the Sun could also be tested.

中文翻译：

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递归整数序列，在以太阳刚性自转数测量的太阳周期周期中检测到

递归数列中的连续整数，斐波那契数列 (F n ) 和卢卡斯数列 (L n )，在从 ≈ 1 年到 ≈ 12 年的太阳活动变化长度中检测到，在太阳的刚性旋转中测量在辐射区的日震学确定的频率下，433 ± 3 $433 \pm 3$ nHz。一圈由符号Ω $\Omega $ 表示。首先，在新的国际太阳黑子数量记录（Ri）中，最频繁（模态）的太阳黑子周期长度，也就是由自相关定义的太阳黑子周期重现周期，为 144 ± ≈ 2 Ω $144 \pm \大约 2~\Omega $ ( F 12 = 144 $\mbox{F}_{12} = 144$ )。循环下降段最常见的长度为 89 ± 2 Ω $\Omega $ (F = 11 89 $_{11} = 89$ )，而上升段为 55 ± 1 Ω $\Omega $ ( F = 10 55 $_{10} = 55$）。其次，在Ω$\Omega $ 的连续L n 数处有一些观测证据表明Ri 谱峰：18 Ω $\Omega $ (≈ 1.3 yr), 29 Ω $\Omega $ (≈ 2.1 yr), 47 Ω $\Omega $ (≈ 3.4 yr) 和 76 Ω $\Omega $ (≈ 5.6 yr)，它们是 144 Ω $\Omega $ 周期除以前四个 F > n 1 $_{{n} } > 1$ : 2, 3, 5, 8. Ω $\Omega $ : 144, 89, 55 可能是从太阳黑子最大值开始的发电机过程中的运动学阈值，当两极改变极性和过程被重新设置。两个连续的 F n 或 L n 的比率收敛到 1 + 5 2 $\frac{1+ \sqrt{5}}{2}$ ，因此表明该比例随着时间的推移在太阳行为中起作用，描述数字上。长度比 1 + 5 2 $\frac{1+ \sqrt{5}}{2}$ 也是空间五重对称的特征。