The Batman Equation Explained

It’s been more than six months since I last posted here, so it’s time for me to write something to prove that I’m still alive.
Recently, there were some talks about a certain mathematical equation in the Internet, whose graph was the famous Batman logo. Some people argued that this was fake and some people reported that it indeed worked. Initially, I had no success in reproducing the graph, after toying around with several free software that could plot graphs of implicit functions. No matter how I entered the equation, the result was not perfect. Therefore, I adventurously decided to analyse the equation and see how it worked. Eventually, I came out with the conclusion that this equation was genuine, but less elegant software may fail to draw certain parts of the graph perfectly due to the complexity aroused from incorporating the visible ranges for the x and y coordinates into the equation.
So, I wrote a whole document to explain how this was done. Both the Chinese and English versions of the document are available for download here in a single ZIP file and the documents are in M$ Word format. It isn’t anything special. I did this only out of boredom.

與上一次發帖比較,已相隔了半年多了,也是時候在這裏寫些東西證明我還在了。
近日,網上流傳了一條可以畫出鼎鼎大名的蝙蝠俠標誌的數學方程,有人認為這是假的,但又有人報告這方程真的可以畫出要求的圖像。在試用多個可繪畫隱函數圖像的免費軟件後,我最初也不能成功作出該圖像,無論我怎樣輸入這方程也無法得出滿意的結果。因此,我決定挑戰一下,對這方程進行分析,企圖找出它是怎樣運作的。我最終得出的結論是這方程是千真萬確的,但較弱的軟件未必能正確地畫出圖像的其中幾個部分。這是因為要在方程中加入有關 xy 坐標的可視範圍的資料,使方程變得複雜了。
為此,我寫了一整篇文章來解釋這方程的意義,其中文版及英文版的 M$ Word 文檔皆已附在這裏的 ZIP 檔。這只是我在納悶時寫的,不是甚麼特別的東西。

batman.zip

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