To Jenkins’ Spoiler-Laden Guide to Isaac Asimov Introduction Though perhaps best known throughout the world for his science fiction, Isaac Asimov was also regarded as one of the great explainers of science. His essays exemplified his skill at making complex subjects understandable, and were written in an unformal style, liberally sprinkled with personal anecdotes that endeared him to a legion of faithful readers. It was all a labor of love; in particular Asimov often remarked that of all his writing, his essays for The Magazine of Fantasy and Science Fiction were his favorite, despite the fact that he received the lowest word-rate payment for them. From November to February , an essay of his appeared in the magazine every month, without fail. With the advent of Isaac Asimov’s Science Fiction Magazine in , he began a series of editorials that appeared at the beginning of each issue. In addition he wrote essays and introductions for literally hundreds of magazines, newspapers, books, and trade publications. All together he wrote over essays.
See Article History Trigonometry, the branch of mathematics concerned with specific functions of angles and their application to calculations. There are six functions of an angle commonly used in trigonometry. Their names and abbreviations are sine sin , cosine cos , tangent tan , cotangent cot , secant sec , and cosecant csc. These six trigonometric functions in relation to a right triangle are displayed in the figure.
For example, the triangle contains an angle A, and the ratio of the side opposite to A and the side opposite to the right angle the hypotenuse is called the sine of A, or sin A; the other trigonometry functions are defined similarly.
Trigonometry in the modern sense began with the Greeks. Hipparchus (c. – bce) was the first to construct a table of values for a trigonometric considered every triangle—planar or spherical—as being inscribed in a circle, so that each side becomes a chord (that is, a straight line that connects two points on a curve or surface, as shown by the inscribed triangle ABC in.
In the adjacent image, the two circles on the map represent lines of position for the Sun and Moon at GMT on October 29, At this time, a navigator on a ship at sea measured the Moon to be 56 degrees above the horizon using a sextant. Ten minutes later, the Sun was observed to be 40 degrees above the horizon. Lines of position were then calculated and plotted for each of these observations.
Since both the Sun and Moon were observed at their respective angles from the same location, the navigator would have to be located at one of the two locations where the circles cross. In most cases, determining which of the two intersections is the correct one is obvious to the observer because they are often thousands of miles apart. As it is unlikely that the ship is sailing across South America, the position in the Atlantic is the correct one. An observer in the Gran Chaco point would see the Moon at the left of the Sun, and an observer in the Madeira point would see the Moon at the right of the Sun.
Angular measurement[ edit ] Using a marine sextant to measure the altitude of the sun above the horizon Accurate angle measurement evolved over the years. One simple method is to hold the hand above the horizon with one’s arm stretched out. The width of the little finger is an angle just over 1. The need for more accurate measurements led to the development of a number of increasingly accurate instruments, including the kamal , astrolabe , octant and sextant.
Sir Isaac Newton
Woolsthorpe, England, 25 December ; d. London, England, 20 March mathematics, dynamics, celestial mechanics, astronomy, optics, natural philosophy. Isaac Newton was born a posthumous child, his father having been buried the preceding 6 October.
NEWTON, ISAAC (horpe, England, 25 December ; , England, 20 March ) mathematics, dynamics, celestial mechanics, astronomy, optics, natural.
Woolsthorpe, England, 25 December ; d. London, England, 20 March mathematics, dynamics, celestial mechanics , astronomy, optics, natural philosophy. Isaac Newton was born a posthumous child, his father having been buried the preceding 6 October. Newton was descended from yeomen on both sides: He was born prematurely, and there was considerable concern for his survival.
He later said that he could have fitted into a quart mug at birth. His early education was in the dame schools at Skillington and Stoke, beginning perhaps when he was five. He was, however, uninterested in farm chores, and absent-minded and lackadaisical. He was admitted a member of Trinity College, Cambridge, on 5 June as a subsizar, and became scholar in and Bachelor of Arts in The rooms he occupied are not known for certain; and we have no knowledge as to the subject of his thesis for the B.
Sunday, January 12, Introducing Logarithms with Foldables, War, Bingo, and Speed Dating Missing three days of school due to the snow and ice really threw off my plans for Algebra 2. I had hoped to get through logarithms before Christmas Break. We did get started with logarithms. But, I had to spend the first four days of the new semester finishing up our logarithm unit.
Students solve exponential and logarithmic equations with their â dateâ in this interactive and self-checking speed dating activity.
The date of the meeting has only been recently been publicised which left us wondering, perhaps erroneously, if this suggested something urgent was to be discussed. The agenda also suggested that the public and press would be barred from some of the discussion. Finally, that same agenda only features two items of significance and these are closely related.
The TfL board, meanwhile, is due to meet on the 17th March. The objective appears to be to achieve world class capacity on these lines by running trains at 36tph — which is a figure genuinely among the best achieved in the world. This is not to say that TfL intends to settle for significantly less on all other lines. On the Central line, in particular, at least a sustainable 34tph should also be possible post-upgrade. Simply that this project relates specifically to the lines named above.
We will look at plans for the World Class Capacity lines in order of complexity and issues involved. This means starting with the Victoria line and then looking at the relatively innocuous plans for the Jubilee, before wading into the issues involving the Northern. These have been replaced with modern trains with decent acceleration and the current state-of-the-art ATO system, which has been a definite success story.
The second method uses a sliding linear L scale available on some models. Addition and subtraction are performed by sliding the cursor left for subtraction or right for addition then returning the slide to 0 to read the result. Standard linear rules[ change change source ] The length of the slide rule is quoted in terms of the nominal length of the scales. Models a couple of meters long were sold to be hung in classrooms for teaching purposes.
Some high-end slide rules have magnifying cursors that make the markings easier to see. Such cursors can effectively double the accuracy of readings, permitting a inch slide rule to serve as well as a inch.
Expanding and Condensing Logarithms Worksheet Lovely Logarithm Properties Speed Dating Activity Condensing and, picture size x posted by at August 26, This specific image (Expanding and Condensing Logarithms Worksheet Lovely Logarithm Properties Speed Dating Activity Condensing and) over is usually classed along with: expanding and, posted through on
Construct viable arguments and critique the reasoning of others. Once students have submitted their responses I will review the answer with the class. Flipchart – solving exponenital equations with logs p. Speed Dating with Log and Exponential Equations 45 minutes Student tutors are the key to the success of this activity. Each student will need their own card. So I was going to just make a double set of copies of these 16 problems. You may also want to have whiteboards and markers available for student work unless you want to collect and analyze their work.
I just want them to have practice solving logarithmic and exponential equations. I am going to ask students to pick up a card as they enter class.
Of course, you would require more than the energy in the whole known universe in order to attain c being massive. The only thing for certain is that the speed of light appears to be constant. In fact no one yet has been able to actually prove it. Einstein would have been better of saying he thinks the speed of light is the fastest thing in the universe. Phaedrus February 19, at 8:
Celestial navigation, also known as astronavigation, is the ancient and modern practice of position fixing that enables a navigator to transition through a space without having to rely on estimated calculations, or dead reckoning, to know their ial navigation uses “sights”, or angular measurements taken between a celestial body (e.g. the Sun, the Moon, a planet, or a star) and.
Sunday, September 11, Significant Figures Speed Dating Activity My physical science students are currently working on determining the correct number of significant figures to use in different situations. The first step is for them to be able to recognize how many significant figures there are in a number. I made posters to hang up in my classroom for them and me! I decided this was the perfect topic to make into a speed dating activity.
You can find the files for my significant figures posters here. To create cards for the speed dating activity, I typed up 20 numbers into a Publisher file.
Student View Task Carbon 14 is a common form of carbon which decays over time. The half-life of Carbon 14, that is the amount of time it takes for half of the Carbon 14 to decay, is approximately years. If there is currently one microgram of Carbon 14 remaining in the preserved plant, approximately when did the plant die?
IM Commentary The task requires the student to use logarithms to solve an exponential equation in the realistic context of carbon dating, important in archaeology and geology, among other places. Note that the purpose of this task is algebraic in nature — closely related tasks exist which approach similar problems from numerical or graphical stances. The two solutions provided differ slightly in their approach in this regard.
Introduction Though perhaps best known throughout the world for his science fiction, Isaac Asimov was also regarded as one of the great explainers of science.
Analog—digital hybrids[ edit ] Analog computing devices are fast, digital computing devices are more versatile and accurate, so the idea is to combine the two processes for the best efficiency. An example of such hybrid elementary device is the hybrid multiplier where one input is an analog signal, the other input is a digital signal and the output is analog. It acts as an analog potentiometer upgradable digitally.
This kind of hybrid technique is mainly used for fast dedicated real time computation when computing time is very critical as signal processing for radars and generally for controllers in embedded systems. In the early s analog computer manufacturers tried to tie together their analog computer with a digital computer to get the advantages of the two techniques.
In such systems, the digital computer controlled the analog computer, providing initial set-up, initiating multiple analog runs, and automatically feeding and collecting data. The digital computer may also participate to the calculation itself using analog-to-digital and digital-to-analog converters. The largest manufacturer of hybrid computers was Electronics Associates.
Their hybrid computer model was made of a digital computer and one or more analog consoles. These systems were mainly dedicated to large projects such as the Apollo program and Space Shuttle at NASA, or Ariane in Europe, especially during the integration step where at the beginning everything is simulated, and progressively real components replace their simulated part. The best reference in this field is the , simulations runs for each certification of the automatic landing systems of Airbus and Concorde aircraft.
One key to the speed of analog computers was their fully parallel computation, but this was also a limitation. The more equations required for a problem, the more analog components were needed, even when the problem wasn’t time critical. Today there are no more big hybrid computers, but only hybrid components.
Math = Love: Introducing Logarithms with Foldables, War, Bingo, and Speed Dating
JEE Mathematics Syllabus Algebra Algebra of complex numbers, addition, multiplication, conjugation, polar representation, properties of modulus and principal argument, triangle inequality, cube roots of unity, geometric interpretations. Quadratic equations with real coefficients, relations between roots and coefficients, formation of quadratic equations with given roots, symmetric functions of roots.
Arithmetic, geometric and harmonic progressions, arithmetic, geometric and harmonic means, sums of finite arithmetic and geometric progressions, infinite geometric series, sums of squares and cubes of the first n natural numbers. Logarithms and their properties. Permutations and combinations, Binomial theorem for a positive integral index, properties of binomial coefficients.
For exponential models, express as a logarithm the solution to ab ct = d where a, c, and d are numbers and the base b is 2, 10, or e; evaluate the logarithm using technology.
Friday, July 29, Growth Mindset Mistakes Poster A continual focus in my classroom is helping my students build a growth mindset. One quote I’ve seen time and time again when it comes to mindset is “Mistakes are expected, respected, inspected, and corrected. This summer, I decided that I wanted to post this on the wall in my classroom as a reminder to students.
I looked online to see if anybody else had already made a poster, but I didn’t see anything that really caught my eye. Though, there might have been a great one that I just missed somehow To be honest, I didn’t spend all that much time looking. Here’s what I came up with: I originally wanted the words at the bottom to be printed on two different colors of paper and be alternated, but I accidentally loaded two sheets of orange paper in my printer.
So, orange it is! Here are close-ups of the different elements: As soon as I can get access to my classroom, I’ll post a picture of them in action! If you’d like to post these in your own classroom, I’ve uploaded the files here as an editable Publisher file and a non-editable PDF file.
Speed Dating: Solving Exp/Log Equations
Does it require more or less effort to push a loaded wheelbarrow over hard level ground than to turn around and pull it? What about when the ground is soft? Surely the clear lens would let the light through rather than casting a shadow? At constant velocity, is this a real effect? If so, wouldn’t it be felt on any “moving” surface you walk on, such as a train or plane — or even Earth? Continued 31 January Pollution resolution If I replace my old diesel car with a less polluting new petrol one, how long will it take for the reduced pollution of the new car to outweigh the increased pollution caused by the manufacture of the new car and the disposal of the old, assuming average usage?
Video: Exponentials, Logarithms & the Natural Log Use the properties of exponentials and logarithms to learn how carbon dating works. This lesson covers properties of a natural log and rules of.
History of Technology Heroes and Villains – A little light reading Here you will find a brief history of technology. Initially inspired by the development of batteries, it covers technology in general and includes some interesting little known, or long forgotten, facts as well as a few myths about the development of technology, the science behind it, the context in which it occurred and the deeds of the many personalities, eccentrics and charlatans involved.
You may find the Search Engine , the Technology Timeline or the Hall of Fame quicker if you are looking for something or somebody in particular. Scroll down and see what treasures you can discover. Background We think of a battery today as a source of portable power, but it is no exaggeration to say that the battery is one of the most important inventions in the history of mankind.
Volta’s pile was at first a technical curiosity but this new electrochemical phenomenon very quickly opened the door to new branches of both physics and chemistry and a myriad of discoveries, inventions and applications. The electronics, computers and communications industries, power engineering and much of the chemical industry of today were founded on discoveries made possible by the battery. Pioneers It is often overlooked that throughout the nineteenth century, most of the electrical experimenters, inventors and engineers who made these advances possible had to make their own batteries before they could start their investigations.
They did not have the benefit of cheap, off the shelf, mass produced batteries. For many years the telegraph, and later the telephone, industries were the only consumers of batteries in modest volumes and it wasn’t until the twentieth century that new applications created the demand that made the battery a commodity item. In recent years batteries have changed out of all recognition. No longer are they simple electrochemical cells. Today the cells are components in battery systems, incorporating electronics and software, power management and control systems, monitoring and protection circuits, communications interfaces and thermal management.