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Mathematical Spirals

According to Wikipedia, a spiral is a curve which emanates from a central point, getting progressively farther away as it revolves around the point (similar to helices [plural for helix!] which are three-dimensional). Pictured above are some of the most important spirals of mathematics.

Logarithmic Spiral: Equation: r=ae^bθ. I must admit that these are my favorite! Logarithmic spirals are self-similar, basically meaning that the spiral maintains the same shape even as it grows. There are many examples of approximate logarithmic spirals in nature: the spiral arms of galaxies, the shape of nautilus shells, the approach of an insect to a light source, and more. Additionally, the awesome Mandelbrot set features some logarithmic spirals. Fun fact: the Fibonacci spiral is an approximation of the Golden spiral which is only a special case of the Logarithmic spiral. 

Fermat’s Spiral: Equation: r= ±θ^(½). This is a type of Archimedean spiral and is also known as the parabolic spiral. Fermat’s spiral plays a role in disk phyllotaxis (the arrangement of leaves in a plant system). 

Archimedean Spiral: Equation: r=a+bθ. The Archimedean spiral has the property that the distance between each successive turning of the spiral remains constant. This kind of spiral can have two arms (like in the Fermat’s spiral image), but pictured above is the one-armed version. 

Hyperbolic Spiral: Equation: r=a/θ. It is also know as the reciprocal spiral and is the opposite of an Archimedian spiral. It begins at an infinite distance from the pole in the center (for θ starting from zero r = a/θ starts from infinity), and it winds faster and faster around as it approaches the pole; the distance from any point to the pole, following the curve, is infinite. 

Ferns

Ferns are more advanced primitive vascular plants. They have true roots, stems, and leaves. Ferns do not have seeds, but produce spores instead. Fern’s lifecycle, unlike primitive non-vascular plants such as bryophytes, is dominated by the sporophyte generation. Some interesting terminology associated with ferns are frond, pinnae, sori, rhizome, and fiddlehead. A frond describes the entire blade of the fern and the smaller individual leaflets are called pinnae. Sori describes clusters of sporangia on the underside of the pinnae (Sori are depicted in the second photo). A rhizome is an underground stem that puts out shoots and adventitious roots. Fiddleheads are furled fronds of a young fern.

Modified Stems: Thorn

Thorns are modified branches or stems. Thorns and spines are derived from shoots and leaves respectively, and have vascular bundles inside, whereas prickles (like rose prickles) do not have vascular bundles inside. The tree shown in the picture above is called the honey locust tree, also known as the thorny locust. Just look at those thorns!

Modified Stems Part:   1     2     3     4     5     6

Minimalist Posters of Great Mathematicians.

I would not sit there. Who knows how much radiation is there 😨

An all-time classic to celebrate St. Valentine’s day! 🤗💘

The five ingredients of a particle accelerator

Did you know there are over 30,000 particle accelerators in the world? The design of particle accelerators is a creative process. Often it starts with just one person and their concept, but they all tend to have 5 key ingredients.

1 - Particles - where do you get them, how do you make them? Accelerators might use atoms with electrons split off, called ions, or the particles inside atoms themselves: electrons or protons.

2 - Energy - you need an acceleration mechanism, some way of giving the particles a push. Typically this uses electric fields.

3 - Control - once your particles are moving, you need to control them, to move them and focus them where they’re needed. This is generally done with magnetic fields.

4 - Collision - not all particle accelerators are ‘colliders’ in the traditional sense. They don’t all collide beams together like at the LHC. But in almost every case you do need to collide your beam of accelerated particles into something - this might be a fixed target to investigate a sample, or even directly into a person’s body, such as during medical treatments.

5 - Detection - there’s normally not much point doing all of this work unless you can then detect the outcome and learn from it. You need to measure what happens to the beam of particles when they collide with their target.

Find out more in our animation about how to design a particle accelerator.

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