Educator How-to: Learn to Draw a Celtic Triquetra

At the Houston Museum of Natural Science, we know that people are as much a part of natural science as rocks and dinosaurs. That’s why we love social studies and maintain exhibits like the John P. McGovern Hall of the Americas and the Hall of Ancient Egypt. We find the development of societies fascinating!

The historical Celts, a diverse group of tribal societies in Iron Age Europe, ranged over a large swath of land reaching as far west as Ireland and the Iberian Peninsula, east to central Anatolia, and north to Scotland. The Celts used a three-cornered symbol, known as the triquetra, to adorn everyday items and important ritual objects. Similar tri-cornered symbols are seen in the artwork of many ancient civilizations. It is speculated that the symbol illustrates the uniting of the past, present, and future or birth, life, death. As Christianity spread through Europe, the triquetra was used to help new converts to understand the concept of the Trinity.

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It is really simple to draw this ancient knot-work symbol. All you need is paper, a compass, an eraser, and some markers.

First, using a compass, draw a circle of at least 3 inches in diameter in the middle of your paper. Make sure to leave room around the circle, as the resulting knot will be slightly larger than the initial circle. Make sure that you do not adjust the compass after the circle is drawn.

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Next, use a pencil to make a point on the circle at the twelve o’clock position. Then, place the point of the compass on this point and use it to make marks where it crosses the circle on each side.   

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Now, place the point of the compass on one of the marks made in the previous step. It doesn’t matter which one. Then, draw a semi-circle within the initial circle. It should start at the twelve o’clock point and end in the lower quarter of the circle. The arc does not need to be continued outside of the circle. Make another arc, identical to the first one. The two arcs should cross at the center point of the circle. If they don’t, check to make sure that the compass setting has not been changed.

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Then, placing the compass point on the lower tailing end of one of the arcs, mark off another tic on the bottom of the circle.celtic5

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Now place the point of the compass on the bottom mark and draw an additional arc from side to side within the circle.

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You will now need to enlarge the diameter of the compass a bit. Place the compass point back onto the marks made in the upper half of the circle. From each point, draw another arc within the circle, and extending a little beyond its border. It is important to make sure the arcs are extend a bit outside of the circle so they’ll meet up when the arcs are all drawn.

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Pick a point where one of the knot strips intersects another, and make it pass over the other, erasing the lines from the underside from within the “over” strip. The next pass for the knot strip, following the same strand, will be to go under the next intersection, so erase appropriately. At this point ,you may erase the initial circle and the arc marks.

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Now your trisquetra is complete! Color it in! See designs like this and others this summer in the Medieval Madness Xplorations Summer Camp.

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Educator How-To: Crystals, Geometry and Chemistry

Math is beautiful and inescapable. Especially in nature, patterns and equations just keep showing up.  The path of an orbiting planet, the growth of a nautilus, arrangements of leaves on a stem, the efficient packing of a honeycomb; we can find rules and algorithms and make predictions from them.

Crystals, with their obediently repeating structure, are an elegant manifestation of the ‘rules.’  To be a crystal, your building blocks (atoms, molecules, or ions) must follow patterns over and over and over and over and over.  Atoms, being predictable, simply do what their chemical properties and the conditions (temperature, pressure, etc.) indicate.  So what exactly does it take to go from a mess of elements and compounds to this example from the Crystals of India exhibit at HMNS Sugar Land?

If you’ve ever tried making rock candy from sugar water or ornaments from borax solution, then you have some idea what it entails: something dissolved that is capable of making crystals has to slowly come out of solution – usually the longer you give it, the bigger it can grow and the slower it grows, the more perfect the crystals.

Freezing water into ice also gives you crystals; they just don’t stick around and let you handle them conveniently at room temperature. Water and solutions in water aren’t the only way to get crystals; molten rock cooling (slowly) can also give crystals, but that’s a little tricky for home experimentation.

So time is your friend for crystal growth, pressure is a factor, and it needs to be easier for atoms to attach to the forming crystal than to stay in solution.  Having a solution that is saturated or supersaturated so it can barely hold all of the dissolved material helps. It also helps to have places for the crystals to start forming; a tiny ‘seed’ crystal or sometimes even just a rough spot on a surface can provide the nucleation sites to kick off crystal growth. Are there other ways crystals and the things we consider ‘gems’ can form? Yes!

For those of us with shorter attention spans, a cool way so see the process is with crystallizing hand warmers – a pouch holds a saturated solution of sodium acetate. When you flex a metal disk inside the pouch, you kick off a chain of crystallization and end up with solid material (and released heat energy).  Because the process is so fast in the hand warmer, the individual crystals are very small and jumbled up (polycrystalline); oriented in all different directions, and as a mass they are opaque (light is refracting all over the place) and relatively dull rather than shiny and smooth as slower-forming large crystal faces can be.  The structure of most metals is also polycrystalline, and things like plastic and glass (even the kinds misleadingly labeled “crystal!”) are amorphous.

The external crystal shapes we see are related to the internal structure – there are a lot of different ways atoms can pack together.

Practically, there will always be some disruption in a crystal structure, no matter how perfect it may appear, which allows for some very cool effects – crystals “twinning,” impurities that alter the color; the reason ruby and sapphire (both corundum crystals) appear different.

Crystals aren’t always pretty! Sometimes we want to prevent crystallization to avoid things like kidney stones, but crystals are useful for all kinds of things; optical equipment and lasers, X-ray crystallography to figure out structures of proteins (and once upon a time, DNA), and silicon chips used in electronic devices. 

Whether you prefer your crystals practical or decorative, they are amazing!

Can’t get enough crystals? Check out the Crystals of India exhibit at HMNS Sugar Land (free for members!)

 

 

I want candy! (boom boom boom ba-dum boom)

Candy can be a useful teaching tool, even if you don’t advocate eating it. It’s well known, comes in lots of varieties, and it’s cheap if you buy it in bulk. It can also be used after its expiration date – great for construction, not consumption. I have used it to illustrate cell and organ structure; architectural design and geometric structures; and, by far my most favorite, dichotomous keys and taxonomy.

Candy Cell Labeled

Test plant cell model

I was first introduced to taxonomy in high school. We had to know the classification of every animal we caught for Marine Biology or dissected in Biology. It wasn’t until college, when we were given the oddest assortment of corks, stoppers, nuts, bolts, nails and screws, that I was introduced to dichotomous keys directly. I am addicted to sorting and organizing, so that assignment was one I thoroughly enjoyed. I had to determine relationships, categorize each “specimen,” name it, and create a key so that anyone could figure out which specimen was which. Loved it!

Years later, in a Texas Master Naturalist training class, an instructor used a simple candy dichotomous key to show us how the key worked before letting us tackle the identification of fish. Have you ever noticed the chin barbels on a croaker? I almost missed them. Dichotomous keys can help scientists to identify field specimen and hopefully new species as well.
The idea to use candy to ease the uninitiated into dichotomous keys was brilliant! So of course I borrowed the idea to use with kids. Now, with kids I kept it simple: “use this key to identify the unknown piece of candy – your ‘specimen.'”

To make sure it worked, I made up names for the candy. Almost everyone knows what a Hershey’s kiss is, but what about Smackus pennsylvius? It’s the name I came up with for the kiss – Hershey’s HQ is in Pennsylvania and in cartoons a kiss comes with a pucker-smack sound, hence Smackus (there are a lot of different Hershey kisses, worth their own genus) and pennsylvius after their origin. You can get a lot more complicated by assigning other species names to each kiss, since they do vary and I assume cannot interbreed. I used the original kiss in the key, so went with the origin for the species name.

Before I get too carried away (and I will) here is a simple key I created for one class. See if you can follow the key below to find the names of Smarties, Jolly Ranchers, Reese’s Peanut Butter Cup, Candy Cane and Mar’s Minis Mix (mixed bag mini Mars brand bars).

Candy samples for dichotomous key

In any dichotomous key, you always start at #1. Like a choose-your-own-adventure story, you are given two paths from which to choose. Each number has 2 choices, or characteristics, that describe the specimen. Each step usually gives you an answer or a direction (go to #3). You may skip a step in a key based on the directions you follow. If your specimen doesn’t fit into either characteristic, go back a step and see if you made the right choice. By observing carefully, you can get the right answers. Of course if your specimen doesn’t fit at all, you may have discovered a new species!

1a. Wrapper is metallic material
1b. Wrapper is non-metallic material
go to #2
go to #3
2a. Shape is circular
2b. Shape is rectangular
Gooberis moosi
Rufusastrum micros
3a. Packaged in groups
3b. Packaged individually
Tarticus owlii
go to #4
4a. Multiple colors present
4b. Multiple colors absent
Noelia crutchii
Bombre merrii

See if you can reason out the names once you have matched them up with their candy. I used my imagination, a good dose of silliness (good for the heart) and some actual Latin roots to come up with these names. The great thing about Latin is you can have a lot of fun trying to pronounce it as well! I’ll give answers if you are interested – please comment.

This is a very basic key; it only lists 5 specimens. which could suggest that there are only 5 species of candy. We know that isn’t the case, but remember that this was for kids and maybe the first time they had tried this.

To actually try and classify (and name) all of the candy you can find in a grocery store gets a lot more complicated. But for someone addicted to classification or candy, it sounds to me like a good time. Happy sorting!