![]() One of these, the autogamous Andean species C. At least four species in the genus were domesticated anciently, either as vegetable or seed crops ( McConnell, 1998). ) Many Chenopodium species are adapted to arid and/or saline environments and are notorious as invasive weed species, including C. (A subset of taxa previously classified in Chenopodium, but having a base chromosome number of x = 8, have more recently been reclassified in the genus Dysphania, as per Mosyakin and Clemants. Most of these species are facultative autogamous annuals, having a base chromosome number of x = 9. The SNPs identified here represent important genomic tools needed in emerging plant breeding programs for advanced genetic analysis of agronomic traits in quinoa.Ĭ henopodium, commonly known as the goosefoot genus, includes a wide array of species native to all inhabited continents. Linkage mapping of the SNPs in two recombinant inbred line populations produced an integrated linkage map consisting of 29 linkage groups with 20 large linkage groups, spanning 1404 cM with a marker density of 3.1 cM per SNP marker. Structure analysis of the quinoa diversity panel uncovered the two major subgroups corresponding to the Andean and coastal quinoa ecotypes. A diversity screen of 113 quinoa accessions showed that the minor allele frequency (MAF) of the SNPs ranged from 0.02 to 0.50, with an average MAF of 0.28. The SNP assays are based on KASPar genotyping chemistry and were detected using the Fluidigm dynamic array platform. We report the identification of 14,178 putative single nucleotide polymorphisms (SNPs) using a genomic reduction protocol as well as the development of 511 functional SNP assays. Efforts to improve the crop have led to an increased focus on genetic research. It is important as a regional food security crop for millions of impoverished rural inhabitants of the Andean Altiplano (high plains). ![]() For example, one author asserts that $\pi = 17 – 8 \sqrt.$$ These formulas are entirely satisfactory to calculate the semiperimeters and areas of inscribed and circumscribed circles, provided one has a calculator or computer program to evaluate tangents and sines.Quinoa ( Chenopodium quinoa Willd.) is an important seed crop throughout the Andean region of South America. One motivation for this article is to respond some recent writers who reject basic mathematical theory and the accepted value of $\pi$, claiming instead that they have found $\pi$ to be a different value. For a step-by-step presentation of Archimedes’ actual computation, see this article by Chuck Lindsey. In this article, we present Archimedes’ ingenious method to calculate the perimeter and area of a circle, while taking advantage of a much more facile system of notation (algebra), a much more facile system of calculation (decimal arithmetic and computer technology), and a much better-developed framework for rigorous mathematical proof. For additional details, see the Wikipedia article. ![]() Indeed, with this method Archimedes anticipated, by nearly 2000 years, the modern development of calculus that began in the 17th century with Leibniz and Newton. But his most far-reaching discovery was the “method of exhaustion,” which he used to deduce the area of a circle, the surface area and volume of a sphere and the area under a parabola. He was a pioneer of applied mathematics, for instance with his discovery of the principle of buoyancy, and a master of engineering designs, for instance with his “screw” to raise water from one level to another. Archimedes is widely regarded as the greatest mathematician of antiquity.
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