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Mobius Strip

3/29/2017

If you are familiar with the concept of infinity, you would recognize its symbol that looks like an eight on its side. That symbol is called a lemniscate, which is Greek for “ribbon”. The lemniscate is directly related to a real-world mathematical shape: the Mobius Strip!

The Mobius strip is particularly fascinating because it is a shape that has only one side and one edge! Let’s compare it to a simple piece of paper: if you draw a line on one side of the paper, there’s nothing on the other side. There are multiple edges to this paper (or just one, if it’s a circle). For a Mobius strip, you can only draw on one side, because there is no other side. If you try to trace your finger along the edge of the strip, you’ll be able to go around and around and around, but it might look like you’re tracing the “other” side, but you never lifted your finger!

This means that a Mobius strip is “non-orientable.” Most objects and surfaces are orientable, and it can be tested by attempting to paint the sides different colors. With a cube, you can have up to six different colors, but with a Mobius strip there’s only one. There’s a famous painting, titled “Mobius Strip II” by M.C. Escher where ants are pictured walking along a Mobius strip. Just like what we’ve described above, the ants (or anything really!) could walk along the strip indefinitely!

The Mobius strip isn’t just some random shape made up for fun; it can actually be applied to real life!

Conveyor belts have used the Mobius strip design, which made it last twice as long. That’s because the entire surface of the strip was used, not just one side got worn down like it would in a normal ring. Manufacturers have stopped using the Mobius strip system because modern-day technology allows multiple layers to support the belt. Typewriters also used the strip’s design in their ribbons. With a ribbon twice as wide as the print head, both halves of the ribbon can be used evenly. This saved a lot of money back when typewriters were popular!

History of the Mobius Strip

In 1858, August Ferdinand Mӧbius invented this shape and named it after himself. John Benedict Listings then independently discovered it and was published following his findings. The two German mathematicians never collaborated, but both are recognized as the strip’s founders. August Mӧbius also singularly discovered the Mobius Ladder, which is an alteration of a prism graph with a twist in it. Another similar mathematical shape is the Klein Bottle, shown below the ladder.

Mobius Experiments!
You can make your very own Mobius strip at home with a piece of paper, some scissors, and tape.

Cut out a strip of paper about 1-2 inches wide
Twist one end halfway
Tape it together

Now you can try out the different examples from before: try to draw a line on “both” sides, or paint them two different colors. If you cut it lengthwise down the middle, what happens? There are many more videos out there that describe other interesting things you can do with a Mobius strip, like this one!

References:

Weisstein, Eric W. "Möbius Strip." MathWorld--A Wolfram Web Resource. Accessed March 25, 2017. http://mathworld.wolfram.com/MoebiusStrip.html
Teplitskiy, Abraham. “Student Corner: Mobius Strip”. The Triz Journal. January 1, 2007. https://triz-journal.com/student-corner-marvel-of-the-mobius-strip. Accessed March 26, 2017.

Image Credits:

Benbennick, David. “Mobius Strip”. Released into the public domain. Uploaded on March 26, 2017 from wikimedia.org
Kapp, J. Lehman. “Endless Belt”. Released into the public domain. Uploaded on March 26, 2017 from US Patent #3991631
Eppstein, David. “Mobius Ladder”. Released into the public domain. Uploaded on March 26, 2017 from wikimedia.org
“Structure of a Klein Bottle”. Released into the public domain. Uploaded on March 26, 2017 from wikimedia.org

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Your Beautiful Skin (And Why Moisture is Important)

3/22/2017

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Your skin is the largest and possibly the most important organ in your entire body. It keeps the rest of your internal organs contained and protects your body from germs and diseases. That’s why taking good care of your skin is essential for a healthy life!

As you can see in the picture above, human skin has many layers and functions. Let’s start at the top with the epidermis. The epidermis is the outermost layer of skin; it creates a waterproof barrier between our bodies and the outside world. It can be very thin in some areas, such as on your eyelids, or it can be thicker like on the bottoms of your feet. The epidermis forms new skin cells at its bottom that travel outward and flake off when they die. It also makes melanin, which is what gives your skin its color.

The dermis is the middle layer of skin and it has many functions. One of its main jobs is making sweat. There are tiny sweat glands dispersed throughout the dermis that make sweat that will then travel to the surface of your skin, using pores as little tubes to travel with. Another type of gland in the dermis is an oil gland. The oil on your skin also comes from your pores, and it helps to keep your skin soft and waterproof. If you aren’t producing enough oils, your skin would dry out and crack, leaving you exposed to outside germs.

Many blood vessels begin in the dermis. They carry blood to your skin to keep it nice and healthy! If you get a scrape or cut deep enough, it will most likely bleed. But your skin isn’t the only thing protecting you, as blood can form a clot around the wound to keep the rest of your blood inside and keep the germs outside. There aren’t any blood vessels in the the epidermis; if you get a bruise, one of your blood vessels was damaged and you’re bleeding a little bit under the first layer of skin.

Other prominent components of the dermis are hair and nerve endings. Humans have nerves all throughout their bodies that help with the sense of touch. Nerves are most sensitive at the nerve endings, which happen to be located in the middle layer of skin. It’s because of the nerve endings there that you are able to feel if something is hot or cold, and rough or soft. You also have little hairs on your skin, all over your body. The dermis is where you’d find the roots of your hair. The hairs grow out of tiny pockets in the dermis, called hair follicles, and is connected to a miniscule muscle that can give you goosebumps when they tighten. Have you ever noticed that bigger scars don’t grow hair? That’s because when the dermis is damaged, so are your hair follicles, so they will no longer allow hair to grow.

The third and bottom layer of skin is called subcutaneous fat. This layer of fat is what connects your skin to your muscles and bones so all of your insides stay inside. Blood vessels that start in the dermis travel through the subcutaneous fat to get to other parts of your body. This fat is also essential to maintaining body temperature and cushioning your bones when you fall or get a bump.

Why is Moisturizing Important?

As mentioned earlier, blood vessels don’t go up to the epidermis, so moisture for your skin has to travel up and out of your skin to evaporate. When that moisture evaporates, it dries out the skin cells in the top layer, leaving them cracked and flaky. Moisturizers can either trap moisture in your skin or replace the moisture that was already lost.

It’s especially important for babies to be moisturized because their skin is much thinner and they have a weaker immune system than adults. It’s also easily irritated and tends to get dry easily. This makes babies uncomfortable, and since they can’t vocalize what they need, they should be moisturized everyday to prevent some skin problems.

There are three main types of moisturizers, classified based on what they’re composed of: occlusives, emollients, and humectants. Occlusives like Vaseline create a barrier over the skin to prevent water from escaping and evaporating. These are often waxes and oils made up of long chains of carbon that are nonpolar, which means they repel water.

Emollients come in the form of ointments, creams, and lotions. These are the type of moisturizers that actually penetrate the skin to keep it soft. They’re composed of the same water-repelling carbon chains as occlusives, but more chemicals are added to make emollients able to sink into skin. This allows them to fill in the spaces between skin cells that have been created when skin gets too dry.

Humectants penetrate the epidermis and attract moisture to it, and lock it in. This is because humectants have a very different chemical structure compared to the other two. They have hydroxyl groups (one oxygen atom and one hydrogen atom) attached to their carbon chains, which are attracted to water. Humectants also prompt the oil glands in the dermis to create more of the skin’s natural moisturizer.

For our activity this week, we recommend you try making your own moisturizer! There are lot’s of great recipes out there, but here's one we recommend. It falls into the occlusives category, so it is a little greasy; we recommend using it at night!

References:

Hoffman, Matthew. "The Skin (Human Anatomy)". WebMD. 16 November, 2014. http://www.webmd.com/skin-problems-and-treatments/picture-of-the-skin#1. Accessed 16 March, 2017.

Image Credits:

Gray, Henry. “The distribution of the bloodvessels in the skin of the sole of the foot”. Released into the public domain. Uploaded on 3/16/17 from wikimedia.org.

Sagdejev, Ildar. “Goose Bumps”. Released into the public domain. Uploaded on 3/16/17 from wikimedia.org.

Daigle, Michelle. “Holding Hands”. Released into the public domain. Uploaded on 3/16/17 from publicdomainpictures.net

Prebreza, Linda. “Applying Lotion”. Released into the public domain. Uploaded on 3/16/17 from pexels.com

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Chemistry of Cooking Part Three: Mushrooms

3/13/2017

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In the past two weeks, we have discussed the science behind pizza: the dough and the sauce. All that’s left is the toppings! In the last post, we learned that popular “vegetables” that we use as pizza toppings are actually fruits, like peppers and olives. But what about mushrooms? They’re not a fruit or a vegetable, mushrooms are part of a completely different group in the fungi kingdom! Neither plant nor animal, fungi are very interesting and complex organisms. Let’s break it down:

What is Fungus?

Fungus is a term used to describe any spore-producing organism that feeds on organic matter, including molds, yeast, mushrooms, and toadstools. That’s right, the yeast from your pizza dough was a fungus as well! Mushrooms are the fleshy, spore-bearing “fruit” of a fungus that grows above ground.

The types of mushrooms you typically find on your pizza have three main parts; a stem, a cap, and gills on the underside of the cap that release spores for reproduction. But the mushrooms are just a small part of a larger fungus that lies underground. Mushrooms start their lives as a little white fluffball underground, and if the environment is humid, nutrients are available, and the temperature is just right, mushroom buds will form and start pushing their way to the surface to find sunlight.

Of the thousands of mushroom species in the world, only about 10% of them are edible. These mushrooms are mass produced on mushroom farms - where a bunch of them can be harvested at once! These are the mushrooms we see and buy at the grocery store, although most of the time, they’re cut in half to make them easier to cook.

Cooking With Mushrooms

Mushrooms are very versatile ingredients - meaning that they can be used in a variety of ways in different kinds of food. They can be boiled, fried, microwaved, grilled, or steamed to prepare them on their own; you can even eat them raw (just be sure they’re very clean)! The only thing you shouldn’t do is wash them in water. Mushrooms will soak up the water and that makes the taste less pronounced.

Some of the most popular types of mushrooms to cook with are portobello, shiitake (pronounced shuh-TALKIE), and the common white or “button” mushroom, like the ones below!

The button mushroom is what you’d typically use as a pizza topping. Just add a handful of mushrooms to the top of your pizza before it goes into the oven, or to enjoy mushrooms as the star of your meal, try making stuffed mushrooms like the ones pictured below. We recommend this recipe from Allrecipies.com for Mouth-Watering Stuffed Mushrooms by Angie Gorkoff!

Image Credits:

Hodan, George. “Small Mushrooms”. Released into the public domain. Uploaded on 3/13/2017 from publicdomainpictures.net

O'Sullivan, Kecia. “Huddled Mushrooms”. Released into the public domain. Uploaded on 3/13/2017 from publicdomainpictures.net

Greyling, Lynn. “Raw Mushrooms”. Released into the public domain. Uploaded on 3/13/2017 from publicdomainpictures.net

Greyling, Lynn. “Mushrooms On The Grid [sic]”. Released into the public domain. Uploaded on 3/13/2017 from publicdomainpictures.net

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Chemistry of Cooking Part Two: Sauce and Vegetables

3/6/2017

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Last week we learned all about pizza dough and how it rises. This week, we’ll take a look at another important part of pizza: the tomato sauce! Or more specifically, the tomato fruit. A lot of people may not know that tomatoes are actually fruits. Between science and cooking, the line between fruit and vegetable is often blurred.

Scientifically speaking, tomatoes are fruits because they develop in the ovary in the base of the flower and contain the plant’s seeds within it. But when using tomatoes to cook, they’re often referred to as vegetables. In fact, many fruits are used as “vegetables” because the food produced is savory instead of sweet. After all, tomato sauce isn’t sweet like applesauce! And while we’re on the subject of fruits and vegetables, it might be nice to know that some other pizza toppings aren’t what they appear to be either. Peppers and olives are fruits too, and mushrooms are neither fruit nor vegetable; they’re actually a fungus!

However, we typically don’t use chunks or slices of tomato as toppings on pizza; we make sauce with them instead! The sauce is like a smoother version of a paste, with added spices and/or herbs. Because of their rich flavor, juiciness, and soft flesh, tomatoes are easy to break down into a sauce that thickens while cooking. Pizza sauce is made with tomatoes, as well as tomato paste. In the activity that follows, we’ll go over how to make pizza sauce with fresh tomatoes, but we’ll just use store-bought paste.

Let’s Make Pizza Sauce!

What you need:

5 pounds of fresh cored whole tomatoes
3 tablespoons extra-virgin olive oil
2 medium onions, chopped
4 cloves garlic, minced
¾ teaspoon dried basil
¾ teaspoon dried thyme
¾ teaspoon dried oregano

1¾ teaspoons salt
½ teaspoon freshly ground pepper
2 tablespoons tomato paste

Step One - Prepare the Tomatoes:

Bring a large pot of water to a boil.
Using a knife, make a small X at the very bottom of each tomato. Plunge the tomatoes into the boiling water and hold there until the skins are loosened (use tongs to protect your own skin!).
Transfer the boiled tomatoes to a bowl of ice water for one minute.
With a paring knife, peel the the tomato’s skin, starting with the X at the bottom.
Chop each tomato, keeping all the juice.

Step Two - Simmer:

Heat the oil in a dutch oven over medium heat.
Add the chopped onions and stir while cooking to a golden brown (about 4-6 minutes). Then add the garlic and cook for an additional minute.
Add the tomatoes (and any juice), basil, thyme, oregano, salt, and pepper. Bring to a boil.
Reduce the heat and simmer until the sauce thickens into the desired consistency (about two hours).
Taste your sauce and season it with more salt and pepper to your liking.

Step Three - Blend:

After simmering, transfer the sauce into a blender. Add the tomato paste and blend until smooth. Be careful when you blend this hot liquid!

Your pizza sauce is now ready! You can cover its container and put it in the refrigerator for up to three days, or freeze the sauce for later use for up to six months!

References:
https://en.oxforddictionaries.com/explore/is-a-tomato-a-fruit-or-a-vegetable
https://www.ncbi.nlm.nih.gov/pubmed/11192026
http://www.compoundchem.com/2014/10/02/tomatoes/
http://www.eatingwell.com/recipe/250096/homemade-pizza-sauce/

Image Credits:

Buissinne, Steve. “Bush Tomatoes”. Released into the public domain. Uploaded on 3/3/2017 from publicdomainpictures.net
Chaffin, Holly. “Pizza Slice”. Released into the public domain. Uploaded on 3/3/2017 from publicdomainpictures.net
Denyer, Circe. “Pizza Sauce”. Released into the public domain. Uploaded on 3/4/2017 from publicdomainpictures.net

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Chemistry of Cooking Part One: Pizza!

3/1/2017

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Most of us eat some type of bread every day, whether it be in the form of toast, sandwiches, dinner rolls, or even pizza dough! For something that seems so simple, why does it take so many different forms?

On the most basic level, all types of bread are made with a grain (typically wheat, but rye, oats, and corn may also be used) and water. Most breads are also made with yeast. There’s a lot of science that goes into the interactions of these ingredients, and variations to recipes are what give bread its unique characteristics.

First, let’s talk about pizza. Or more specifically, its dough. Pizza dough is made with four simple ingredients:

Bread flour
Water/oil mixture
Yeast
Salt

Once all of the ingredients mix, you’ll want to let the dough sit and rise for about an hour. But why does this happen? You can thank yeast for making your bread fluffy and your pizza crust soft.

Yeast are single-celled fungi that are mass produced for baking, in the form of tiny beige granules.

The yeast lies dormant until it meets water, and then it begins to consume the sugars in the flour. You could say that as the yeast are eating the sugar, they start to burp, thus releasing their carbon dioxide!

This process, called yeast fermentation, gives off carbon dioxide, which are the little bubbles that make your dough rise. Another byproduct of yeast fermentation is ethanol, but that gets boiled off during baking.

The other important ingredient in bread dough is salt. Aside from adding flavor, salt also acts to slow down the fermentation process so the dough rises gradually instead of all at once. It also strengthens the bread’s gluten structure.

What is Gluten?

The type of flour that we use to make bread is called wheat flour. Wheat flour contains the proteins glutenin and gliadin, which form gluten when combined with water. As the dough is kneaded, the gluten proteins are uncoiled and become stretchy. It now has the texture of gum, which is what traps the little bubbles of carbon dioxide from the yeast and prevents the gas from escaping.

Once the dough has been left to rise, it’s time to form it into whichever type of bread you’re making. For pizza, you’d roll it out into a thin circle. For a regular loaf of bread, it’s easy to shape into a blob and place it in a bread pan. When you finally bake the dough, yeast will continue to do its job and let the bread rise and the pockets of gas will continue expanding until the temperature gets too high and all the yeast dies. One of the last things that happens is that the gluten hardens so that your dough solidifies, becoming bread!

Make Dough!

What you need:

2 and ¼ teaspoons yeast
1 and ⅓ cups warm water
3 and ½ cups flour, plus more as needed
2 tablespoons olive oil
⅔ teaspoon salt
1 tablespoon sugar

Steps:

In a large mixing bowl, combine water and yeast. Stir and let sit for about five minutes, or until the yeast is foamy and dissolved.
Add oil, flour, salt, and sugar, and mix together for about a minute
Once all ingredients are thoroughly mixed, knead the dough on a flat surface dusted with flour for about 7-8 minutes. Dough is ready when it is smooth and elastic. Poke it with your finger to see if it slowly bounces back into shape.
Put the rolled up ball of dough back in the bowl, with oil covering the sides of the bowl. Cover tightly with plastic wrap and allow the dough to rise for an hour and a half in a warm place. Check on the dough every once in a while to see how it rises!
After retrieving the dough, punch it down to let some air out. Divide the dough into two smaller pieces. One of these will make a 12-inch pizza crust. Set the dough aside for about fifteen minutes while you get your pizza toppings ready.
On a lightly floured flat surface, flatten and stretch the dough into a 12-inch circle. Lift up the edges to create a lip for the pizza crust.
Once you’ve added your favorite toppings, bake your pizza for 12-15 minutes at 475℉.

References:

http://www.compoundchem.com/2016/01/13/bread/
https://www.exploratorium.edu/cooking/bread/bread_science.html
http://redstaryeast.com/homemade-pizza-crust/

Image credits:

Kratochvil, Petr. “Italian Pizza”. Released into the public domain. Uploaded on 2/26/2017 from publicdomainpictures.net.

Nyren, Erin (2014). “Yeast Fermentation Processes”. Discovery Express Kids, LLC.

Kratochvil, Petr. “Raw Dough”. Released into the public domain. Uploaded on 2/26/2017 from publicdomainpictures.net.

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Mobius Strip

﻿Your Beautiful Skin (And Why Moisture is Important)

﻿Chemistry of Cooking Part Three: Mushrooms

Chemistry of Cooking Part Two: Sauce and Vegetables

Chemistry of Cooking Part One: Pizza!

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Your Beautiful Skin (And Why Moisture is Important)

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