The Problem Solved

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When you look through your viewfinder and things seem a little bit blurry or lacking definition, it’s probably because you are using an “el cheapo” lens. Which leads to countless You Tube reviews on lenses. In a 1949 article published in the Royal Society Proceedings, Wasserman and Wolf formulated the problem—how to design a lens without spherical aberration—in an analytical way, and it has since been known as the Wasserman-Wolf problem.

So you read reviews and buy a much more expensive lens, and what do you do next? They “proposed to use two aspheric adjacent surfaces to correct spherical and coma aberrations, with a solution consisting of two first-order simultaneous differential equations, which are solved numerically according to Malacara-Hernández et al.” In other words, the solution was an approximation solved with numerical analysis (brute-force with computers), not a definitive one.

The Levi-Civita problem, which has existed without a solution for over a century, was also considered a mythical problem by the specialized community. (via Tec de Monterrey) About the author: Eduardo Machuca is Yet-Another-Photographer that taught for eight years at both the bachelor’s and master’s degree level in advertising photography.

It is important to note that both solutions—the Wasserman-Wolf problem and the Levi-Cita problem—are analytical, with symbolic math. He lives, and has always lived, in Mexico, and loves traveling around the hood and taking care of his alebrijes, with the help of an alux.Afterwards, the duo ran a simulation and calculated the efficacy with 500 rays, and the resulting average satisfaction for all examples was 99.9999999999%. Even though lenses will be cheaper to manufacture, remember that once somebody stamps the “made for photographers” sticker on a product, it is priced many times higher because of the “added value” to your artistry.Which, of course, is great news for gear reviewers on You Tube, as they will still be able to argue about the 0.0000000001% of sharpness difference among lens brands. Regardless, I can only wish Rafael González-Acuña, Alejandro Chaparro-Romo and Julio Gutiérrez-Vega a long and healthy life.To this day, when you see that your lens has aspherical elements to correct for optical aberrations and give you sharper images wide open, you can thank Wasserman-Wolf.However, the importance of solving this problem goes well beyond giving you a sharper picture of your feet for your nine Instagram followers. Chaparro-Romo, a doctoral student at the National Autonomous University of Mexico (UNAM), who had been trying to solve this problem for 3 years, invited Rafael G.In this episode, IISE web editor David Brandt chats with IISE Fellow and ISE magazine columnist Kevin Mc Manus about the discipline of Essentialism and what it has in common with industrial engineering.They also discuss the various ways ISEs apply best practices for continuous improvement in both career and personal life. Blame Greek mathematician Diocles, who formulated the problem over two thousand years ago in his book . The problem arises when light rays outside the center of the lens or hitting at an angle can’t be focused at the desired distance in a point because of differences in refraction. But it’s not the manufacturer’s fault, nor yours for not having enough money to buy a perfect an innovative mathematical problem-solving series providing students with opportunities to apply their numeracy skills in order to solve problems.The problem-solving process will vary from student to student and from problem to problem.


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