March 7, 2016
An excellent overview of the multitude of active theories and hypotheses–like quantum gravity, string theory–physicists are investigating to try to explain the universe.
From Theories on Everything Mapped
In the quest for a unified, coherent description of all of nature — a “theory of everything” — physicists have unearthed the taproots linking ever more disparate phenomena. With the law of universal gravitation, Isaac Newton wedded the fall of an apple to the orbits of the planets. Albert Einstein, in his theory of relativity, wove space and time into a single fabric, and showed how apples and planets fall along the fabric’s curves. And today, all known elementary particles plug neatly into a mathematical structure called the Standard Model. But our physical theories remain riddled with disunions, holes and inconsistencies. These are the deep questions that must be answered in pursuit of the theory of everything.
–Natalie Wolchover in Theories of Everything Mapped on Quanta Magazine.
Citing this post: Urbano, L., 2016. Physics: Theories of Everything (Mapped), Retrieved February 23rd, 2017, from Montessori Muddle: http://MontessoriMuddle.org/ .
Attribution (Curator's Code ): Via: ᔥ Montessori Muddle; Hat tip: ↬ Montessori Muddle.
Posted in PhysicsNo Comments »  Tags: interactive websites, modern physics, physics
September 5, 2014
A couple of my students asked for worksheets to practice drawing atoms and electron shells. I updated the Atom Builder app to make sure it works and to make the app embedable.
So now I can ask a student to draw ^{23}Na^{+} then show the what they should get:
Worksheet
Draw diagrams of the following atoms, showing the number of neutrons, protons, and electrons in shells. See the example above.
 ^{14}C^{}: answer.
 ^{32}K^{+}: answer.
 ^{18}O^{2}: answer.
 ^{4}He^{2+}: answer.
 ^{32}P^{–}: answer.
I guess the next step is to adapt the app so you can hide the element symbol so student have to figure what element based on the diagram.
Citing this post: Urbano, L., 2014. Updated Atom Builder, Retrieved February 23rd, 2017, from Montessori Muddle: http://MontessoriMuddle.org/ .
Attribution (Curator's Code ): Via: ᔥ Montessori Muddle; Hat tip: ↬ Montessori Muddle.
Posted in Chemistry, Interactive, Natural World, Programming1 Comment »  Tags: apps, atoms, atoms and molecules, chemistry apps, css5, html5, interactive web apps, interactive websites, javascript, kineticjs
January 22, 2013
This app lets you drag and drop electrons, protons, and neutrons to create atoms with different charges, elements, and atomic masses. You can also enter the element symbol, charge and atomic mass and it will build the atom for you.
Note, however, it only does the first 20 elements.
Citing this post: Urbano, L., 2013. Atom Builder, Retrieved February 23rd, 2017, from Montessori Muddle: http://MontessoriMuddle.org/ .
Attribution (Curator's Code ): Via: ᔥ Montessori Muddle; Hat tip: ↬ Montessori Muddle.
Posted in Chemistry, Interactive, Natural World, ProgrammingNo Comments »  Tags: apps, atoms, atoms and molecules, chemistry apps, css5, html5, interactive web apps, interactive websites, javascript, kineticjs
March 7, 2012
So that my students could more easily check their answers graphically, I put together a page with a
more complete analysis of parabolas (click
this link for more details).
Analyzing Parabolas
Solution by Factoring:
y = x^{2} x
Converting the forms
The key relationships are the ones to convert from the
standard form of the parabolic equation:


(1) 
to the
vertex form:


(2) 
If you multiply out the vertex equation form you get:

y = a x^{2}  2ah x + ah^{2} + k 
(3) 
When you compare this equation to the standard form of the equation (Equation 1), if you look at the coefficients and the constants, you can see that:
To convert from the vertex to the standard form use:
Going the other way,
To convert from the standard to the vertex form of parabolic equations use:
Although it is sometimes convenient to let k not depend on coefficients from its own equation:


(10) 
The Vertex and the Axis
The nice thing about the vertex form of the equation of the parabola is that if you want the find the coordinates of the vertex of the parabola, they're right there in the equation.
Specifically, the
vertex is located at the point:


(11) 
The axis of the parabola is the vertical line going through the vertex, so:
The equation for the axis of a parabola is:


(12) 
Focus and Directrix
Finally, it's important to note that
the distance (d) from the vertex of the parabola to its focus is given by:


(13) 
Which you can just add
d on to the coordinates of the vertex (Equation 11) to get the
location of the focus.


(14) 
The directrix is just the opposite, vertical distance away, so the
equation for the directrix is the equation of the horizontal line at:


(15) 
References
There are already some excellent parabola references out there including:
Citing this post: Urbano, L., 2012. Everything You (N)ever Wanted to Know About Parabolas, Retrieved February 23rd, 2017, from Montessori Muddle: http://MontessoriMuddle.org/ .
Attribution (Curator's Code ): Via: ᔥ Montessori Muddle; Hat tip: ↬ Montessori Muddle.
Posted in Algebra, Mathematics, Technology, Useful websitesNo Comments »  Tags: algebra, graphing interactives, graphs, html5, interactive posts, interactive websites, math, polynomials
September 24, 2011
Cyclohexane, from the interactive model on 3Dchem.com.
Molecular models tend to fascinate. As a introduction to the chemistry of elements, students seem to like putting them together, and they tend to enjoy finding out what their molecules are called.
You can't beat fitting together molecules by hand as a learning experience, but
3Dchem has a nice
collection of interactive, threedimensional molecules, including
molecules of the month.
Periodic spiral of the elements (from 3Dchem.com).
They also have threedimensional periodic tables showing the sizes of the atoms in the traditional tabular form as well as a
spiral.
Periodic Table showing the elements by size.
Citing this post: Urbano, L., 2011. 3d Molecule of the Month, Retrieved February 23rd, 2017, from Montessori Muddle: http://MontessoriMuddle.org/ .
Attribution (Curator's Code ): Via: ᔥ Montessori Muddle; Hat tip: ↬ Montessori Muddle.
Posted in Chemistry, Natural World, Useful websitesNo Comments »  Tags: 3d models, interactive websites, molecules, periodic table