Final answer:
All dates of the Shire-reckoning are calculated from the year of the Fall of Sauron at the end of the Third Age, corresponding to 3021 of the Third Age in Tolkien's Middle-earth. This is a fictional calendar used by Hobbits and is not linked to real historical events.
Step-by-step explanation:
All dates of the Shire-reckoning are calculated from the year of the Fall of Sauron, which marks the end of the War of the Ring and the beginning of the Fourth Age in J.R.R. Tolkien's Middle-earth legendarium. This year corresponds to 3021 of the Third Age in the Shire-reckoning. It is important to note that Shire-reckoning is a fictional calendar system used by the Hobbits in Tolkien's works and does not correspond to any real historical dating system.
In the real world, the establishment of calendar systems often involved astronomical observations and complex calculations, as seen with the relative chronology of Zhou kings or the dating of events in history by means of carbon-14 dating and other methods. Such methods helped historians establish timelines for events like the battle of Muye in 1045 BC.