From Shouldn’t We Teach GEOMETRY?, Branko Grunbaum, The Two-Year College Mathematics Journal, Vol. 12, No. 4 (Sep., 1981), pp. 232-238
I will read anything by Grunbaum.
Women in Science Interactive
Women in Science, a new interactive tool, presents the latest available data for countries at all stages of development. Produced by the UNESCO Institute for Statistics, the tool lets you explore and visualize gender gaps in the pipeline leading to a research career, from the decision to get a doctorate degree to the fields of research women pursue and the sectors in which they work.
The Google doodle celebrates Percy Julian on Friday, April 11, 2014.
Percy Lavon Julian (April 11, 1899, Montgomery, Al. – April 19, 1975, Waukegan, Illinois) was a U.S. research chemist and a pioneer in the chemical synthesis of medicinal drugs from plants.He was the first to synthesize the natural product physostigmine, and a pioneer in the industrial large-scale chemical synthesis of the human hormones, steroids, progesterone, and testosterone, from plant sterols such as stigmasterol and sitosterol. His work would lay the foundation for the steroid drug industry’s production of cortisone, other corticosteroids, and birth control pills.
He later started his own company to synthesize steroid intermediates from the Mexican wild yam. His work helped greatly reduce the cost of steroid intermediates to large multinational pharmaceutical companies, helping to significantly expand the use of several important drugs.
During his lifetime he received more than 130 chemical patents. Julian was one of the first African-Americans to receive a doctorate in chemistry. He was the first African-American chemist inducted into the National Academy of Sciences, and the second African-American scientist inducted from any field.
Ruggedized scientific calculator perfect for extreme math
By Tim Hornyak, IDG News Service
It laughs at splashes, dust and shocks. It eats military-spec drop tests for breakfast. It’s ideal for math in the great outdoors.
Meet Casio’s new ruggedized scientific calculator, the fx-FD10 Pro.
Mainly aimed at land surveyors, the device has 21 programs for civil engineering purposes such as curve calculations for plotting road construction.
The 250-gram FD-10 Pro is housed in an elastomer-coated case so it won’t slip out of a user’s hands, even when wet.
It’s got a backlit LCD screen for working in low light, an SD card slot for importing data from surveying equipment and a USB port to link with PCs. A series of side keys allow users to operate it with one hand.
It meets U.S. military standard 810G for shocks, and can be dropped from a height of 1.22 meters without damage, according to Casio.
“We don’t know of any leading calculator manufacturer who sells a rugged scientific calculator,” a Casio spokeswoman said. “It’s the first Casio scientific calculator to have all three features of being shock resistant, splash-proof and dust-proof.”
The model is being launched to meet anticipated demand for construction related to the Olympics in Tokyo in 2020. The Japanese capital has been considering everything from a futuristic 80,000-seat stadium to a gondola lift as part of its makeover for the games.
Growing infrastructure demand in developing economies was another factor behind the launch, the spokeswoman added.
The FD-10 Pro will go on sale on April 25 in Japan, and is expected to sell for around ¥24,000 ($235).
The calculator is also to be marketed in many ASEAN (Association of Southeast Asian Nations) countries, but launch dates will differ.
Casio is considering selling the FD-10 Pro worldwide as well, the spokeswoman said.
The Fluctuating Math Errors in Americans’ Tax Returns
4:40 PMApr 15 By Mona Chalabi
Seeing as Tuesday night is the deadline for filing tax returns, and seeing as data is FiveThirtyEight’s raison d’être, I was excited to find a set of statistics titled “Math Errors on Individual Income Tax Returns, by Type of Error.” Even better, that data has been published for tax years from 2001 to 2012.
It’s unsurprising that some Americans make mistakes on their taxes; the 1040 form (the primary tax form) has 77 line items, as well as a 189-page appendix of instructions. But Internal Revenue Service data shows that math mistakes — potentially an indication of how confusing that form is — have changed a lot over time.
Why does the number of errors fluctuate so much?
We called the IRS, and apparently we weren’t the first to do so. Anthony Burke of the IRS media relations team said, “I’ve asked those [IRS tax] folks about that before, and I’ve never really got a clear answer about why the numbers are doing that.”
Burke did, however, point us toward the first-time homebuyer credit, which was introduced in 2009. Maybe the credit caused confusion, and as a result, more mistakes? But the biggest increase in math errors happened in 2008, not 2009. In any case, the IRS attributed only 132,550 math errors to the homebuyer credit in 2009: 1 percent of the total.
But that did prompt us to take a closer look at changes in tax credits. The first-time homebuyer credit, Hope and American Opportunity Education credits, and Making Work Pay credit didn’t exist before the 2009 tax year. And the recovery rebate credit didn’t exist before the 2008 tax year. Those new credits provided new opportunities to make mistakes.
It turns out that the recovery rebate credit caused a lot of confusion. In 2008, 10,032,780 math errors occurred specifically with respect to that credit. So that explains the spike in 2008. But in 2009, there were only 877 mistakes on the recovery rebate credit. Instead, the Making Work Pay credit was causing trouble; it led to 6,412,242 errors. And if change is a source of confusion, then tax code reforms in 2001 could also explain the high number of errors that year.
Developments within the IRS may also play a role. A report from the Government Accountability Office in 2003 found that changes in math errors since 1996 were attributable to “statutory changes that expanded the types of issues the IRS could address with non-audit programs, declines in IRS enforcement staffing, and priorities in using staff.”
Moving from facts to theory, the decrease in errors since 2009 might also partly be explained by the increase in use of TaxACT, TaxSlayer, TurboTax and other online filing services. That assumes that such providers are less prone to mistakes than alternative solutions, such as Americans calculating their own taxes or using traditional accountants. The National Taxpayers Union has claimed that is not a safe assumption.
See How Cadbury Hatches 350 Million Goo-Filled Eggs a Year
By Elise Craig
Candy company Mondelēz International only sells Cadbury Créme Eggs from January through Easter, but its factories fill chocolate shells with gooey cream 364 days a year. It’s the only way to ensure 350 million eggcellent candies are ready for their plastic-grass-lined baskets. Easter shift manager (his actual title) Charles McDonald shows us how the Cadbury factory in Birmingham, England, achieves candy magic, ova and ova.
1 | Mix: Cadbury trucks in chocolate crumb, a sandy paste made from reduced cocoa liquor, milk, and sugar. Two mills grind the particles down and machines fold in cacao butter, warming the mixture to just above body temperature. The factory goes through one ton of chocolate every hour, 24 hours a day.
2 | Coat: A depositor funnels chocolate into eggcups on hinged trays (96 indentations on each side). The trays shake as they move, helping the liquid chocolate to pool in the depressions.
3 | Cream: The white and yellow fillings are made of sugar, water, glucose, and a proprietary goo called “blended syrup”—and free-range-egg powder. Why? “I think it’s a historic thing,” McDonald says. The “white” and the “yolk” have nearly identical ingredients, but the yellow contains food coloring.
4 | Fill: The chocolate-filled trays run under the cream depositor, which squirts in the white goo. The dense cream pushes the pooled chocolate up the sides of the mold. Next, the depositor shoots a smaller quantity of yellow stuff into the center; the yolk is denser than the white, so the two parts of the egg don’t mix.
5 | Cool: To make the still-wet half-eggs whole, the mold-closing machine snaps the trays shut, “like closing a book.” Air coolers solidify the eggs—slowly, to make sure a white bloom doesn’t form on the surface.
6 | Wrap: Once the eggs have hardened, a wheel picks up each one and spins it 360 degrees while small mechanical arms smooth the foil onto the surface.
Scale-Free Mathematics in Matzah?
By Samuel Arbesman
Tonight is Passover. And the most well-known food of the holiday is matzah, the cracker-like flatbread. Within this food we can find some complexity science goodness.
At one part of the Seder meal, we break one piece of matzah into half. Now, for anyone who has actually tried this, one recognizes the great difficulty in doing so. Matzah does not break evenly. It too often breaks along fracture points that cause a piece of matzah to break into small pieces, large pieces, and everything in between. If you’re familiar with the principle of crackling noise and universality in physics, this should sound familiar.
There are many systems, that when tuned in a certain way, reach a critical threshold where something changes. For example, when ice melts or a magnet is heated to lose its magnetism, these things occur when a specific temperature is reached. But at that specific parameter’s value—such as zero degrees for ice—the properties of the system can have a certain scale-free or self-similar nature.
For example, take the canonical example from percolation theory:
Percolation theory is the study of the connectivity of networks. If you take a piece of paper and punch small holes in it at random positions, it will remain connected if the density of holes is small. If you punch so many holes that most of the paper has been punched away, the paper will fall apart into small clusters.
There is a phase transition in percolation, where the paper first falls apart. Let p be the probability that a given spot in the paper has been punched away. There is a critical probability p_c below which the paper is still connected from top to bottom, and above which the paper has fallen into small pieces (say, if it is being held along the top edge).
At that critical value, below which everything is connected and above which the paper is in small pieces, you often get pieces of all sizes. Essentially, there is no scale—it’s scale free.
And perhaps that’s what’s happening with matzah: a piece of matzah is in a carefully tuned critical state, allowing it to crack into pieces of all sizes. Further research and discussion is necessary, of course, and are both fitting topics for a Seder discussion.