TABUNGAW

THE MATHEMAGICAL TABUNGAWS OF GAWAD SA MANLILIKHA NG BAYAN
GINOONG TEOFILIO GARCIA

Garcia 1

Keep your eyes open while walking around Banguet and you may be lucky enough to spot Teofilo Garcia on one of his weekly shopping trips to town. He will be very easy to recognize as he will be wearing his unique Tabungaw hat, which he wears each time he leaves home. Teofilo Garcia is a simple man, still a farmer at heart and since he was bestowed the title of “Gawad sa Manlilikha ng Bayan” (National Living Treasure) he has been invited to give talks and demonstrations in the Philippines and abroad, teach local school children the art of Tabungaw making, and open up his home/workshop to drop in visitors who wish to meet him and buy one of his unique products.

The Art of Tabungaw Hat Making

Tabungaw 1

The hat called a Kattukong is weatherproof and made from Upo (tagalog) or Tabungaw (Ilocano), also known as Bottle Gourd or White Pumpkin which are part of the Cucurbitaceae family of plants. Each December the seeds are planted and three to four months later in March the crop is harvested and brought down to his workshop to be cured and dried. The gourds are cut open using a hand saw and the two halves placed on the ground by his house. They are left there for about a month while nature takes over. Ants are attracted to the rotting pulp and help to clean the insides leaving the case empty. It is then finished by hand and left to dry completely. Only the upper half is used to make the Tabungaw. The bottom half can be used around the house for various storage purposes. After drying, the Tabungaw is then coloured and varnished. Any blemishes in the gourd are left in place and not hidden, adding to its attractive look. The most time consuming and skillful part comes next. That is the weaving of the bamboo inner casing and lining. The woven interior is made of anahaw, nipa, bamboo, and/or rattan. Only around one hundred Kattukong are made each year with each Tabungaw taking on average 7 days to transform into a hat which will last a lifetime if taken care of properly. Locally the hat is also known as “Strongkis”

Tabungaw Design Optimization

The activity below to optimize volume. For a cone volume is: Vc=43πr2h . Notice that the coefficients for each of the polynomial terms is as denoted in the activity as well. The question then becomes: Which coefficient value was changed to result in the largest increase in volume?

Instructions for activity

Start the following interactive applet by clicking on the image below. After waiting a moment for it to load, you will see a 3d mathematical depiction of a Tabungaw. Your job is to press play on each of the coefficient sliders one t a time. Note how the volume of the Tabungaw changes. Your assignment is to find the value of each coefficient that MAXIMIZES the value of the Tabungaw's volume. Make a note of each coefficient value as well as the final value of the maximized volume. Report to the class and compare volumes to see whose volume is greatest, and share the coefficient values for this to the class. Then drag and rotate the Tabungaw with your mouse to see the shape of the one with the greatest volume.

Activity 1

Self-Assesment questions

Mathematical "Profile Function" Analysis

The generating function (function P(x) within the closed interval [a,b]) for the Tabungaw profile is as follows: $$P(x)=\textbf c_4x^4+\textbf c_3x^3+\textbf c_2x^2+\textbf c_1x+\textbf c_0x$$

Activity 2

PRE-CALCULUS ACTIVITY

Click image directly below if you are a Pre-Calculus or Honors Algebra II student

Activity 2

CALCULUS ACTIVITY

Click image directly below if you are an Honors or AP Calculus student

Activity 2

CONCLUSION

The National Living Treasures Award, alternatively known as the Gawad sa Manlilikha ng Bayan (GAMABA; lit. 'Award for the Creators of the Country'), is conferred to a person or group of artists recognized by the Government of the Philippines for their contributions to the country's intangible cultural heritage. A recipient of the award, a National Living Treasure or Manlilikha ng Bayan is "a Filipino citizen or group of Filipino citizens engaged in any traditional art uniquely Filipino, whose distinctive skills have reached such a high level of technical and artistic excellence and have been passed on to and widely practiced by the present generations in their community with the same degree of technical and artistic competence."

You can find out more about it here or here!