Search results
Results From The WOW.Com Content Network
Bt maize / Bt corn is a variant of maize that has been genetically altered to express one or more proteins from the bacterium Bacillus thuringiensis [8] including Delta endotoxins. The protein is poisonous to certain insect pests. Spores of the bacillus are widely used in organic gardening, [9] although GM corn is not considered organic.
Removing five axioms mentioning "plane" in an essential way, namely I.4–8, and modifying III.4 and IV.1 to omit mention of planes, yields an axiomatization of Euclidean plane geometry. Hilbert's axioms, unlike Tarski's axioms, do not constitute a first-order theory because the axioms V.1–2 cannot be expressed in first-order logic.
As of 2016, major crop (soybean, maize, canola and cotton) traits consist of herbicide tolerance (95.9 million hectares) insect resistance (25.2 million hectares), or both (58.5 million hectares). In 2015, 53.6 million ha of Genetically modified maize were under cultivation (almost 1/3 of the maize
Birkhoff's axiomatic system was utilized in the secondary-school textbook by Birkhoff and Beatley. [2] These axioms were also modified by the School Mathematics Study Group to provide a new standard for teaching high school geometry, known as SMSG axioms. A few other textbooks in the foundations of geometry use variants of Birkhoff's axioms. [3]
Absolute geometry is a geometry based on an axiom system consisting of all the axioms giving Euclidean geometry except for the parallel postulate or any of its alternatives. [69] The term was introduced by János Bolyai in 1832. [70] It is sometimes referred to as neutral geometry, [71] as it is neutral with respect to the parallel postulate.
Chapter two is titled "Affine and Projective Geometry". Artin posits this challenge to generate algebra (a field k ) from geometric axioms: Given a plane geometry whose objects are the elements of two sets, the set of points and the set of lines; assume that certain axioms of a geometric nature are true.
Theodor Spieker (8 August 1823 – 9 April 1913) was a German mathematician, a teacher at a gymnasium in Potsdam. [1]Spieker's geometry textbook Lehrbuch der ebenen Geometrie mit Übungs-Aufgaben für höhere Lehranstalten (Verlag von August Stein, Potsdam, 1862) [2] [3] was republished in many editions.
For some other divergent geometric series, including Grandi's series with ratio −1, and the series 1 + 2 + 4 + 8 + ⋯ with ratio 2, one can use the general solution for the sum of a geometric series with base 1 and ratio , obtaining , but this summation method fails for 1 + 1 + 1 + 1 + ⋯, producing a division by zero.