Seeing Functions at the City Museum

October 31, 2012

The slide on the third floor of the City Museum. A co-ordinate system is overlayed, and points showing the curve of the slide are selected.

Elegant curves.

I asked my students to take pictures of the curves they found while on our field trip to the scrap metal playground that is the City Museum. The plan is to see if we can determine what functions best fit the curves. To do so, we need to transfer the curves from the images to a co-ordinate system. Since I’m primarily interested in what type of functions might best fit the data, the scale of the co-ordinates does not matter that much.

Feet, inches, meters, centimeters, pixels, or any other units can be used. In fact, I use a purely arbitrary set of coordinates in the image above. All I require is that the grid be evenly spaced (although the vertical and horizontal spacing don’t have to be the same, it’s more straightforward if they are).

Now we take a set of points that lie on our shape and try to match them to some sort of curve using a spreadsheet, and, if we’re able, least squares regression.

There were lots of shapes to choose from.

There were lots of shapes to choose from, including the nice sinusoid in the background.

Citing this post: Urbano, L., 2012. Seeing Functions at the City Museum, Retrieved April 21st, 2018, from Montessori Muddle: .
Attribution (Curator's Code ): Via: Montessori Muddle; Hat tip: Montessori Muddle.

Spring Wildflowers at the Shaw Nature Reserve

April 8, 2012

Spring blooms (possibly of Royal Catchfly -- Silene regia) at the Shaw Nature Reserve

I took a half-day trip during spring break (somewhere around the 31st) to the Shaw Nature Reserve in Gray Summit. I was hoping to find some books on native, Missouri, flora and fauna, and see if the Reserve would be a good place for a field trip (they have sleeping facilities so even overnight trips are a possibility).

I found a number of books, including a nice one on mushrooms, and while I could have, I did not pick up one on wildflowers (of which there were several). Of course, spring is the perfect time to see wildflowers, especially since we ended up hiking the Wildflower Trail, so I’m probably going to have to go back sometime soon.

The lady at the main office (where you pay $5/adult) recommended we take the Wildflower Trail and then cut down south to the sandbar on the Meramec River, which is an excellent place for skipping rocks. She also recommended I take my two kids to their outdoor “classroom” for some real, unstructured play.

View Shaw Nature Reserve – Wildflower Trail in a larger map

Without a reference book, I’ve had to resort to the web for identifications, with only a little success, so I’ll post a few of my photographs here and update as I identify them.

The following two pictures are of a flower that was found covering the hillslope meadows; open areas with short grass.

Beautiful reddish-orange blooms on this small herb.

This picture better captures the growth form and leaves of this hillslope, meadow flower.

A yellow petalled variant.

Like little stars in the daylight, these small, white flowers meadow flowers almost sparkle.

Small, white, meadow flowers.

Pretty, small, yellow, meadow flowers.

Yellow, meadow flowers.

These bent-over flowers can be found on the lower, shadier edges of the hillslope meadows.

These guys like the shadier areas.

I love the texture of the charred wooden stump behind the flower. The meadow itself is possibly the result of a burn.

Iris’ were also in bloom.

Small iris.

Another herbaceous, yellow flower.

Pretty yellow flowers.

More, tiny, delicate flowers.

Found in the shadier, moister parts of of the slope.

Once you get under the canopy, you run into some broader leaved plants and their own, interesting flowers.

Bell-shaped flowers in broad-leaved herbs/shrubs.

We ended up spending a lot of time on the sandbar, learning to skip rocks and hunting for clams, but I save that for another post. And we never did get to the play area; that’ll have to wait for the next trip.

Citing this post: Urbano, L., 2012. Spring Wildflowers at the Shaw Nature Reserve, Retrieved April 21st, 2018, from Montessori Muddle: .
Attribution (Curator's Code ): Via: Montessori Muddle; Hat tip: Montessori Muddle.

The Physics of Flight: World Bird Sanctuary in St. Louis

March 13, 2012

Bird of Prey -- at the World Bird Sanctuary.

A discussion of the physics of flight, interspersed with birds of prey swooping just centimeters from the tops of your head, made for a captivating presentation on avian aerodynamics by the people at the World Bird Sanctuary that’s just west of St. Louis.


The presentation started with the forces involved in flight (thrust, lift, drag and gravity). In particular, they focused on lift, talking about the shape of the wings and how airfoils work: the air moves faster over the top of the wind, reducing the air pressure at the top, generating lift.

The shape of a bird's wing, and its angle to the horizontal, generates lift. Image adapted from Wikipedia User:Kraaiennest.

Then we had a demonstration of wings in flight.

Terror from the air.

We met a kestrel, one of the fastest birds, and one of the few birds of prey that can hover.


Next was a barn owl. They’re getting pretty rare in the mid-continent because we’re losing all the barns.

Barn owl.

Interestingly, barn owls’ excellent night vision comes from very good optics of their eyes, but does not extend into the infrared wavelenghts.

Barn owl in flight.

Finally, we met a vulture, and learned: why they have no feathers on their heads (internal organs, like hearts and livers, are tasty); about their ability to projectile vomit (for defense); and their use of thermal convection for flying.

The ground warms when it absorbs sunlight (e.g. parking lots in summer) and in turn warm the air near the ground. Hot air rises, creating a convection current, or thermal, that the vultures use to gain height.

The Sanctuary does a great presentation, that really worth the visit.

Citing this post: Urbano, L., 2012. The Physics of Flight: World Bird Sanctuary in St. Louis, Retrieved April 21st, 2018, from Montessori Muddle: .
Attribution (Curator's Code ): Via: Montessori Muddle; Hat tip: Montessori Muddle.

Impressions of Monet

January 4, 2012

Nympheas, by Claude Monet. Image via Wikipedia.

We took the middle and high school to see the Monet Water Lilies exhibit at the St. Louis Art Museum today. It was a nice tour; we saw some paintings, and we learned a little something about the impressionists.

One thought that occurred to me during an interesting conversation on the bus back to school, was how the development of abstract thinking skills affects our perception of the more abstract art. After all, it usually requires more effort to appreciate, understand and become affected a piece the more abstract it is. Which would suggest that art appreciation would be useful practice for adolescents who are honing their higher-level cognitive skills.

The tour also left me with one unanswered question, however: are we seeing fog or smog in Monet’s painting of the Charing Cross Bridge in London.

Charing Cross Bridge by Monet. Image via Wikipedia.

London is famous for its fogs, but this painting was done in 1899, well into the industrial revolution, and the yellow tints suggest a pea-souper.

Citing this post: Urbano, L., 2012. Impressions of Monet, Retrieved April 21st, 2018, from Montessori Muddle: .
Attribution (Curator's Code ): Via: Montessori Muddle; Hat tip: Montessori Muddle.

Coal Seam

December 29, 2011

Escavator digs out the coal.

Although it was high in sulfur, the quarry company mined the thin coal seam that cut across the limestone quarry/landfill.

The water cycle, at the quarry.

The layer of coal is pretty impervious to water, so it blocks vertical infiltration of water, which forces the water to the surface as springs.

At the surface, when the water is exposed to oxygen in the atmosphere, dissolved iron precipitates to produce a red mineral that stains the quarry walls.

The iron gets into the water when pyrite crystals (FeS2) in the coal dissolves. While the iron precipitates, the sulfur remains in the water, making it more acidic. Dealing with the acid can be a huge problem in large coal and metal mines.

The pool of water that collects at the base of the quarry, is probably fairly acidic.

Not all the pyrite is dissolved however, and since this particular coal seam has a lot of pyrite, it is not economical to burn since the burnt sulfur (as sulfur dioxide gas) would have to be captured — otherwise it produces acid rain.

The rich black coal seam sits on top of blocky limestone rock. Above the limestone is a red, weathered soil.

Citing this post: Urbano, L., 2011. Coal Seam, Retrieved April 21st, 2018, from Montessori Muddle: .
Attribution (Curator's Code ): Via: Montessori Muddle; Hat tip: Montessori Muddle.

The Water Cycle … at the Quarry

December 15, 2011

The water cycle, at the quarry.

The water cycle is intricately tied to all the other topics that came up on our visit to the quarry/landfill. For some things, the tie to water is direct and inextricable.

  • It’s groundwater that dissolves the pyrite in the coal seam and then precipitates an orange iron stain on the quarry cliffs.
  • Rainwater seeping into the landfill leaches out chemicals that have to be prevented from getting into the groundwater, rivers or lakes.
  • Gases like hydrogen sulfide can react with water (and oxygen) in the air to produce acid rain. Not to mention that water is needed for the decaying processes that produce the hydrogen sulfide, and other landfill gases like methane, to begin with.

For other things the link to water is not necessarily so obvious:

  • The sediment that was compressed into the limestone that is being quarried, was formed beneath the shallow seas that once covered this region in the geologic past. Limestone is also dissolved by rainwater to create caverns, underground rivers and spaces for geodes.
  • Methane gas not only requires water for it to be released via decomposition of garbage, but also produces carbon dioxide when burned. Carbon dioxide is a greenhouse gas, so it affects the global temperature and contributes to the melting glaciers, rising sea levels and changes in climatic patterns such as the amount of rain we’re going to receive in the midwest.

The water cycle picture starts simply, but gets complicated very quickly.

A bigger, fuller picture of the water cycle as it interacts with the quarry.

Citing this post: Urbano, L., 2011. The Water Cycle ... at the Quarry, Retrieved April 21st, 2018, from Montessori Muddle: .
Attribution (Curator's Code ): Via: Montessori Muddle; Hat tip: Montessori Muddle.

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