Concavity and Convexity of Red Bean Soup

Manek, Eh Lee and I had a lively discussion on the definition of concavity and convexity. Our views were significantly different. To settle the argument, we turned to research. The prize for the winner: bragging rights and a pot of tong sui (Chinese soup-ish dessert).

I have always thought that concave means something that is hollowed in and convex the exact opposite.

This is what I have learnt from my research so far.

concaveconvex.jpg

Source: Amazing Space

However, I have noted that the concave and convex functions in calculus appear inconsistent with my views.

concaveconvexfunction.jpg

Source: Wolfram Mathworld

Further reading revealed the following: 

In calculus, a differentiable function f is convex on an interval if its derivative function f ′ is increasing on that interval: a convex function has an increasing slope. Similarly, a differentiable function f is concave on an interval if its derivative function f ′ is decreasing on that interval: a concave function has a decreasing slope.

A function that is convex is often synonymously called concave upwards, and a function that is concave is often synonymously called concave downward.

Source: Answers.com

The conclusion I have reached is that technically, I am right with regards to the general definitions of concavity and convexity. What puzzles me is why mathematicians named functions with decreasing slopes as concave and vice versa. Explanations anyone?

I have never made red bean soup in my life. The extent of my kitchen knowledge and cooking repertoire is limited to maggie mee and boiled eggs. Since I am totally useless around the kitchen, I decided to attempt:

The Making of anttyk’s Red Bean Soup!!!

Be afraid, be very afraid.

Firstly, the ingredients.

  1. Red beans (doh!) soaked in water overnight.
  2. Small sago.
  3. Pandan leaves.
  4. Sugar lumps from sugar cane.
  5. Dried winter melon (cheating).

Cook the red beans in half a pot of water for two hours. Remember to include a china spoon in the pot while cooking the red beans. The spoon is to add flavour to the whole dessert (haha) – the years of accumulated grime, grease and goodnessknowswhat on the spoon handles sure is flavoursome. At the end of two hours, add the washed and tied up pandan leaves, the dried winter melons and two lumps of sugar into the concoction. Simmer for another 1 hour.

img_4343ed.jpg

Boil some water in a separate pot to cook the sago. Stir the sago gently so that they don’t clump together. The sago will become transparent when cooked perfectly. This takes about 20 minutes. Remove the sago from the pot with a sieve and soak them in cold water.

img_4345ed.jpg

When the red bean soup is ready to serve, add the sago into the pot. Bring to boil once. It’s ready for eating.

img_4353ed.jpg

Me so proud of myself. *pats back… pats some more… pats Seekarlui for helping… pats everybody around… pat pat pat pat pat…*

Mum will be so proud too.

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5 Responses

  1. This is all too complex for me. I no understand. Next time can put colour pictures instead ah? Or pictures of cute footie players 😀

    anttyk: Sure thing Lily. 🙂

  2. *drools* no red bean soup for us?

    anttyk: If you are good, I’ll make some for you and Hamsterbit.

  3. Send some over to Singapore… Jules and I can share…. muahahaha

    anttyk: Watch me stick out my tougue and wave it at you…. Pfffbbrrttt! 🙂

  4. This is what u call a friend… sigh…..

    anttyk: Sayang, sayang… *pats head* Merajuk ye… Kesian…

  5. Gossh..so complicated ler the way you cooked the red bean dessert =p..nehhh nvm first timer..kekeke..try put “gula melaka” next time…

    anttyk: :p

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