An Intuitive Guide To Exponential Functions & e

e has always bothered me — not the letter, but the mathematical constant. What does it really mean? The mathematical constant e is the base of the natural logarithm. And when you look up natural logarithm you get: The natural logarithm, formerly known as the hyperbolic logarithm, is the logarithm to the base e, where e is an irrational constant approximately equal to 2.718281828459. Nice circular reference there. I’m not picking on Wikipedia — many math explanations are dry and formal in their quest for rigor. No more! e is NOT Just a Number Describing e as “a constant approximately 2.71828…” is like calling pi “an irrational number, approximately equal to 3.1415…”. Pi is the ratio between circumference and diameter shared by all circles. e shows up whenever systems grow exponentially and continuously: population, radioactive decay, interest calculations, and more. Understanding Exponential Growth Let start by looking at a basic system that doubles after an amount of time. A Closer Look Mr.

Math Expression: Free Math Tutor Online Introduction - 10,000 Year Clock The full scale 10,000 Year Clock is now under construction. While there is no completion date scheduled, we do plan to open it to the public once it is ready. The essay below by Long Now board member Kevin Kelly discusses what we hope the Clock will be once complete. This is one of several projects by Long Now to foster long-term thinking in the context of the next 10,000 years. by Kevin Kelly There is a Clock ringing deep inside a mountain. is around to hear it. The Clock is real. The Clock is now being machined and assembled in California and Seattle. The Clock’s inventor introduced the idea of the Clock (in 01995) with this context: I cannot imagine the future, but I care about it. That’s Danny Hillis, a polymath inventor, computer engineer, and designer, inventor and prime genius of the Clock. Eno also composed the never-repeating melody generator that rings the Clock’s chimes inside the mountain. To see the Clock you need to start at dawn, like any pilgrimage. You keep climbing.

Newton Raphson The Newton Raphson method does not need a change of sign, but instead uses the tangent to the graph at a known point to provide a better estimate for the root of the equation. Here our new estimate for the root is found using the iteration: Note: f'(x) is the differential of the function f(x). (This equation is essentially saying you must divide the y-value by the gradient, and subtract this from the previous estimate.) Repeat the process until the root is found to the desired degree of accuracy. Example: Lets take the equation f(x) = ex − 3x. Differentiating this gives f'(x) = ex - 3. Let's estimate that the root to this equation is 0.6. Then a better estimation of the answer will be given by the Newton Raphson equation: We can take this better estimation and put it through the Newton Raphson equation again to get an even more accurate solution: As this gives the same solution, it must be the correct root for the equation (to 3 decimal places).

Math and English: free printable math materials in English for mative students and ESL math students. Fallacy List 1. FAULTY CAUSE: (post hoc ergo propter hoc) mistakes correlation or association for causation, by assuming that because one thing follows another it was caused by the other. example: A black cat crossed Babbs' path yesterday and, sure enough, she was involved in an automobile accident later that same afternoon. example: The introduction of sex education courses at the high school level has resulted in increased promiscuity among teens. 2. example: Muffin must be rich or have rich parents, because she belongs to ZXQ, and ZXQ is the richest sorority on campus. example: I'd like to hire you, but you're an ex-felon and statistics show that 80% of ex-felons recidivate. 3. example: All of those movie stars are really rude. 4. example: What's the big deal about the early pioneers killing a few Indians in order to settle the West? 5. 6. example: Either you favor a strong national defense, or you favor allowing other nations to dictate our foreign policy. example: It’s not TV. 7. 8. 9. 10. 11.

Interactive Whiteboard Resources: Maths, Key Stage 2 - Topmarks Education Caterpillar OrderingTablet friendly A flexible game for ordering numbers and for number sequences. Fantastic on an interactive whiteboard and tablet friendly. OrderingFlash You'll love this ordering game! Compare Numbers on a Number LineFlash Compare numbers on two different number lines and decide which is bigger. Comparing NumbersFlash A teaching tool which is good for demonstrating greater than and less than with 2 and 3 digit numbers and rounding to 10 and 100. CountersquareFlash A hundred square with movable counters and lots of different ideas on how you can use this as a teaching aid. Higher and LowerFlash Lots of examples of ordering numbers from simple ordering numbers to 10 to fractions, decimals or negative and positive numbers. Thinking of a NumberFlash Children need to guess a number below 100 from clues on the clouds. Chinese Dragon GameTablet friendly Chinese Dragon Game is an ordering and sequencing numbers game based on the Chinese New Year dragon theme. SequencesFlash

Personal and Historical Perspectives of Hans Bethe