# Magnifying Power to the People with the Foldscope

The microscope holds a place on the short list of inventions that have changed the world and revolutionized our understanding of science. Microscopes are crucially important public health tools, allowing workers to identify pathogens and correctly diagnose the cause of illnesses. As educational tools, they can excite and engage students, revealing a world invisible to the naked eye. And, as many people who’d love a microscope but don’t have one can tell you, they are also expensive. Millions of doctors, health workers, and patients worldwide lack the resources to benefit from this vital tool, and millions of students have never seen a microscope before. In a dramatic step to address this problem, researchers from Stanford University have designed ultra-low-cost microscopes built from an inexpensive yet durable material: paper. They recently published their designs and data in PLOS ONE.

Meet the Foldscope. Borrowing from the time-honored tradition of origami, the Foldscope is a multi-functional microscope that can be assembled much like a paper doll. Users cut the pieces from a pattern of cardstock, fold it according to the printed lines, and add the battery, LED, and lens, and?voilà?a microscope. Click here to watch a video of how one is assembled. Some of their coolest features are as follows:

• Foldscopes are highly adaptable and can be configured for bright-field and dark-field microscopy, to hold multiple lenses, or to illuminate fluorescent stains (with a special LED).

• They can be designed for low or high powers and are capable of magnifying an image more than 2,000-fold.
• They accept standard microscope slides, and the viewer can move the lens back and forth across the slide by pushing or pulling on paper tabs.
• Users can focus the microscope by pushing or pulling paper tabs that change the lens’ position.
• Foldscopes are compact and light, especially when compared with conventional field microscopes. They also weigh less than 10 grams each, or about the weight of two nickels.
• They are difficult to break. You can stomp on them without doing much damage, and they can survive harsh field environments and encounters with children.

What’s the total cost, you ask? According to authors, it’s less than a dollar.  At that price, it’s easy to imagine widespread use of Foldscopes by many who previously could not afford traditional microscopes. In this TED Talk, Manu Prakash demonstrates the Foldscopes and explains his hopes for them. The authors envision mass producing them and distributing different designs optimized for detecting the pathogens that cause specific diseases, such as Leishmaniasis and E. coli.  They could even include simple instructions for how to treat and prepare slides for specific diagnostic tests or provide pathogen identification guides to help health workers in the field make diagnoses.  This is just one way in which the ability to see tiny things could make a huge difference in the world.

Low-Cost Mobile Phone Microscopy with a Reversed Mobile Phone Camera Lens

Community Health Workers and Mobile Technology: A Systematic Review of the Literature

Citation: Cybulski JS, Clements J, Prakash M (2014) Foldscope: Origami-Based Paper Microscope. PLoS ONE 9(6): e98781. doi:10.1371/journal.pone.0098781

Images: Images are from Figures 1 and 2 of the published paper

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# The Tyranny of Pi day

March 14th is $$\pi$$-day in the US (and perhaps $$4.\overline{666}$$ day in Europe). The idea of a day devoted to celebrating an important irrational number is wonderful — I’d love to see schools celebrate e-day as well, but February 71st isn’t on the calendar. Unfortunately, March 14th has also become the day in which 4th and 5th graders around the US practice for one of the most pointless exercises imaginable – a competition to recite the largest number of digits of $$\pi$$.

Memorization of long digit strings is not an exercise that teaches a love of mathematics (or anything else useful about the natural world).  This is solely an exercise in recall, which is perhaps valuable for remembering phone numbers, but not for understanding transcendental constants. For all practical purposes, only the first few digits of $$\pi$$ are really necessary – the first 40 digits of $$\pi$$ is enough to compute the circumference of the Milky Way galaxy with an error less than the size of an atomic nucleus.

So, because $$\pi$$ is a such an accessible entry to mathematics and science, I thought I’d come up with a list of other cool $$\pi$$ things that could replace these pointless memory contests:

• The earliest written approximations of $$\pi$$ are found in Egypt and Babylon, and both are within 1 percent of the true value. In Babylon, a clay tablet dated 1900–1600 BC has a geometrical statement that, by implication, treats $$\pi$$ as 25/8 = 3.1250. In Egypt, the Rhind Papyrus, dated around 1650 BC, but copied from a document dated to 1850 BC has a formula for the area of a circle that treats $$\pi = \left(\frac{16}{9}\right)^2 \approx 3.1605$$.
• In 220 BC, Archimedes proved that $$\frac{223}{71} < \pi < \frac{22}{7}$$.  The mid-point of these fractions is 3.1418.
• Around 500 AD, the Chinese mathematician Zu Chongzhi  was using a rational approximation for $$\pi \approx 355/113 = 3.14159292$$, which is astonishingly accurate.  For most day-to-day uses of $$\pi$$ this particular approximation is still sufficient.
• By 800 AD, the great Persian mathematician, Al-Khwarizmi, was estimating $$\pi \approx 3.1416$$
• A good mnemonic for the decimal expansion of $$\pi$$ is given by the letter count in the words of the sentences: “How I want a drink, alcoholic of course, after the heavy lectures involving quantum mechanics. All of thy geometry, Herr Planck, is fairly hard…”
• Georges-Louis Leclerc, The Comte de Buffon came up with one of the first “Monte Carlo” methods for computing the value of $$\pi$$ in 1777.  This method involves dropping a short needle of length $$\ell$$ onto lined paper where the lines are spaced a distance $$d$$ apart.  The probability that the needle crosses one of the lines is given by:  $$P = \frac{2 \ell}{\pi d}$$.
• In 1901, the Italian mathematician Mario Lazzarini attempted to compute $$\pi$$ using Buffon’s Needle.  Lazzarini spun around and dropped a 2.5 cm needle 3,408 times on a grid of lines spaced 3 cm apart. He got 1,808 crossings and estimated $$\pi = 3.14159292$$. This is a remarkably accurate result!   There is now a fair bit of skepticism about Lazzarini’s result, because his estimate reduces to Zu Chongzhi’s rational approximation.  This controversy is covered in great detail in Mathematics Magazine 67, 83 (1994).
• Another way to estimate $$\pi$$ would be to use continued fractions.  Although there are simple continued fractions for $$\pi$$, none of them show any obvious patters.  There’s a beautiful (but non-simple) continued fraction for $$\frac{4}{\pi}$$:
$$\frac{4}{\pi} = 1 + \frac{1^2}{2 + \frac{3^2}{2 + \frac{5^2}{2 + \frac{7^2}{2 + …}}}}$$

Can you spot the pattern?

• Vi Hart, the wonderful mathemusician, has a persuasive argument that we should instead be celebrating $$\tau$$ day on June 28th.   Actually, all of her videos are wonderful.  If my kids spent all day doing nothing but playing with snakes  it would be better than memorizing digits of $$\pi$$.
• Another wonderful way to compute $$\pi$$ is to use nested round and square baking dishes (of the correct size) and drop marbles into them randomly from a distance.  Simply count up the number of marbles that land in the circular dish and keep track of the total number of marbles that landed in either the circle or the square. Since the area formulae for squares and circles are related, the value of $$\pi = 4 \frac{N_{circle}}{N_{total}}$$.

There are probably 7000 better things to do with $$\pi$$ day than digit memory contests. There are lots of creative teachers out there — how are all of you going to celebrate $$\pi$$-day?

# The Up-Goer Five Research Challenge

I thought this was silly at first, but after struggling to do it for my own research, I now think it can be a profound exercise that scientists should attempt before writing their NSF broader impact statements. Here’s the challenge: Explain your research using only the 1000 most common English words. Here’s a tool to keep you honest: http://splasho.nfshost.com/upgoer5/  The idea was inspired by Randall Munroe’s wonderful Up Goer Five explanation of the Saturn V moon rocket.

And here’s my attempt:

The things we use every day are made of very tiny bits. When we put lots of those bits together we get matter. Matter changes how it acts when it gets hot or cold, or when you press on it. We want to know what happens when you get some of the matter hot. Do the bits of hot matter move to where the cold matter is? Does the hot matter touch the cold matter and make the cold matter hot? We use a computer to make pretend bits of matter. We use the computer to study how the hot matter makes cold matter hot.

The task is much harder than you think.   Here’s a collection curated by Patrick Donohue (a PhD candidate in lunar petrology right here at Notre Dame):  Common words, uncommon jobs