In ancient China , values for π included (around 1 AD), √ 10 (100 AD, approximately ), and 142 / 45 (3rd century, approximately ). [54] Around 265 AD, the Wei Kingdom mathematician Liu Hui created a polygon-based iterative algorithm and used it with a 3,072-sided polygon to obtain a value of π of . [55] [56] Liu later invented a faster method of calculating π and obtained a value of with a 96-sided polygon, by taking advantage of the fact that the differences in area of successive polygons form a geometric series with a factor of 4. [55] The Chinese mathematician Zu Chongzhi , around 480 AD, calculated that π ≈ 355 / 113 (a fraction that goes by the name * Milü * in Chinese), using Liu Hui's algorithm applied to a 12,288-sided polygon. With a correct value for its seven first decimal digits, this value of ... remained the most accurate approximation of π available for the next 800 years. [57]

The essay titles we have discussed so far have largely been those you might use for an academic essay, or the type that involves research of some sort. However, it is very likely that you might be asked to write a title about a descriptive essay, an imaginative piece, or a personal piece. In fact, it is probably true to say that these areas of writing are more likely to involve you in the process of evolving a title, since they are, in a sense, more creative. If you are asked to create a title of this sort, again, try to write a list of your ideas about the topic because these might generate a title for you. This time, however, your focus needs to be very much on capturing the attention of your reader, just as a headline does in a newspaper, to make them want to read on. Examples of titles that might be applicable to each of the above are: