LIMACONS (lee-mah-songs)

LIMACONS

IN a faraway land where imagination runs wild, there lives a civilization of Spider People. According to some lesser known and perceived "wacko" mathematicians and believers of the fantastic, they are described as having the upper half of a human and the lower half a body of a spider. Yes, the form may be grotesque, but they are, as these mathematicians say, the wisest and most intelligent of all mythical creatures for the art of weaving and spinning webs is to them a most sacred art. They are ruled by a loving King and Queen, who rules with hearts of gold and brains of justice , intellect, and truth.

The spider people excel in this sacred art, and part of this art is the spinning of thick lines, circles, various functions anyone can name, hyperbolas, parabolas, sine waves, tangent series, roses, spirals, lemniscates, floors, ceilings, other graphs one can name, and butterflies---yes, even butterflies. Every spider person is required to master spinning of these figures in a thin and transparent web by the reasonable age of adulthood.

But alas, asketh ye of the limaçon, they know not.

In this land lives an orb-weaver Spider Princess called Whitey. The bards sing of her as "White hair, silver eyes, beautiful and fair in ev'ry way." With her two hands, eight slender legs, and versatile spinnerets tucked within her abdomen, she crafts and weaves the best, the most intricate, and sometimes the most complex of "graphs".

In this same land, but in the outskirts of their Domain, lives Blackey. He was branded a Disjoint not because of his male black widow spider body, black hair, green eyes, and fair skin but because he never mastered any of the "graphs" mentioned above, and he had tried to, but all were sloppy attempts. None did know, however, that he was a master at the one "graph" nobody ever knew how to spin: limaçons.

But how did this simple graph change the entire history of their Domain? Here is how.

It was a normal sunny day, just like a day for real life students taking Precalculus as their math requisite in college. Whitey, wearing her traditional white T-shirt, wanted to explore the outer regions of their Domain, and got her wish that day when she was able to explain the principles of the land: all sides and corners of this imaginative land approach infinity. She was walking around the shabby houses of the Outcasts spaced evenly apart and placed at angles no trigonometric law can explain.

She headed towards the marketplace, for the most exquisite of smells and tastes were sold in this market. She entered the market and jovially explored the area (and her spinnerets twitched thrice every time she felt a rush of positive emotions). Meanwhile, Blacky was running towards his friend's store to see if the herbs he ordered were in stock. Little did he know that the Princess was right in front of his friend's store, and so the both of them crashed into each other and fell to the ground.

"I'm sorry," Whitey said as she stood up, "It's my fault. I didn't see where I was going." "No, it's my fau-ault!" Blacky replied, but after he saw whom he was dealing with, he bowed prostrate in front of her. Whitey giggled a little, and then asked him to stand up.

"I was just going to ask Skylar if the herbs have arrived," Blacky admitted, "I didn't see you there." "Yes, they have, Blacky," the female proprietor replied as she packed up his request and handed it to him. "Thanks, Skylar!" he said, "Well, Princess, I have to leave now." Then, he skittered off quickly.

"Who was that?" Whitey asked. "That's my friend and fellow Outcast, Blacky. He is quite famous in this town of Outcasts," Skylar replied. "Why?" the princess asked. "He makes the best limaçons around."