User:MeganBontogon

Homework 12

Food Science

A very interesting topic, both food science and calculus related is the process of wine making. After the grapes have been harvested, crushed, and pressed (in the case of white wines), they undergo the process of fermentation.

To begin this process yeast is added. The existing population of yeast cells at a given point in the fermentation process can be given as a function of time.

This is an example of a function expressing the population of yeast cells in a wine vat over a period of days.

Graph Showing Population of Yeast Cells In a Wine Vat

This function explains the growth and decline of the yeast population in the fermentation process of wine.

The yeast colony undergoes steady growth in ideal aerobic conditions in the first stage of the fermentation.

Stage 2 of the fermentation process involves anaerobic conditions which are unfavorable to the survival of the yeast and the cells die off, and fall to the bottom of the barrel.

This is shown as the function begins to decrease rapidly. When making white wines, they are allowed to settle and the dead yeast cells gather at the bottom of the barrel.

In red wines, they are fermented with their skins on so the skins must be pressed and the yeast is filtered out right away.

The sweetness of the wine depends on how long it is allowed to ferment. If the yeast completely converts all the sugar in

the grapes to alcohol, you will get a dry wine; if the process is stopped earlier you will be able to make a sweeter wine.

Generally speaking, most of the wines with a higher level of sweetness have a lower alcohol content.

The alcohol content of wines are approximated using a hydrometer. This chart displays the specific gravity reading of the

hydrometer, the initial amount of sugar in the wine, and the percentage alcohol possible if all the sugar is converted to alcohol by the yeast.

Hydrometer Chart

The values in this chart could also be represented by the amount of sugar as a function of the possible percentage of alcohol. These are just some examples of calculus in wine making. Mathematics can also be involved in the ratios of ingredients to produce certain flavors and aromas.

PYTHAGOREAN THEOREM

The pythagorean theorem was said to be discovered in Egypt by Pythagoras, an ancient Greek who was studying there(Benson 2009). However the true origin of the theorem is unknown because it is also possible that the ancient egyptians had already discovered it(Benson 2009). The Pythagorean theorem applies to right angle triangles only. Each triangle is made up of two legs and a hypotenuse. "The word 'hypotenuse' comes from two Greek words meaning 'to stretch'(Benson 2009)." This attributes to the hypotenuse being the longest side of the triangle(Benson 2009). Another thing that sets the hypotenuse apart from the two legs is that it is always the side opposite the right angle. The theorem states that the values of each leg of the triangle are squared and then their sum equals the value of the hypotenuse squared. This can be shown as $a^{2}+b^{2}=c^{2}$. This formula can then by used to find the values of a missing side given the values of the other 2 sides. For Example, when given the value of the hypotenuse as 5, and one of the legs as 3, the missing value for the other side can be found by subbing in the values:

                            $3^{2}+b^{2}=5^{2}$
                             $9+b^{2}=25$
                                $b^{2}=16$
                                $b=sqrt(16)$
                                $b=4$

So then the value for the missing leg of the triangle is 4.

References:

Benson, Tom.2009.Pythagorean Theorem.Glenn Research Center, Nasa.<http://www.grc.nasa.gov/WWW/K-12/airplane/pythag.html>