Proof of the Assertion that Any Three Non-Collinear Points Determine Exactly One Circle This is an interesting problem in geometry, for a couple of reasons. First, you can apply some earlier, basic geometry principles; and secondly, you can choose two different strategies for solving the problem. The basic geometry underlying: any three non-collinear points determine a plane, somewhere in 3D space. Once that has been done, imagine that the plane has been rotated into the x-y plane, which will make the problem much easier to solve! The two strategies for solution are: (Proof A) actually solve to find the circle. This is equivalent to finding the center of the circle (finding the equation of the circle is simple from there). But, you actually have to do some math to get this! If, while doing this, there is no possibility to obtain other values for the coordinates of the center of the circle, you have proved the assertion as well as obtained a method (and perhaps... read more
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Suppose, one have two parallel lines given by the equations: y=mx+b1 and y=mx+b2. Remember, if the lines are parallel, their slopes must be the same, so m is the same for two lines, hence no subscript for m. How would one approach the problem of finding the distance between those lines? First, if one draws a picture, he or she shall immediately realize that if a point is A chosen on one of the lines, with coordinates (x1, y1), and a perpendicular line is drawn from that point to the second line, the length of the segment of this new line between two parallel lines give us the sought distance. Let us denote the point of intersection of our perpendicular line with the second line as B(x2,y2). What do we know of point A and B? First, since A lies on the first parallel line, its coordinates must satisfy the equation for the first line, that is, y1=mx1+b1 (1) Same is true for B and the second line. So we can write: y2=mx2+b2... read more
This is another way to find a distance between two parallel lines. This derivation was suggested to me by Andre and I highly recommend him and his answers to any student, who wants to learn math ans physics. This derivation requires the knowledge of trigonometry and some simple trigonometric identities, so this may be suitable for more advanced students. Once again, we have two lines. y=mx+b1 (1)--equation for the first line. y=mx+b2 (2)--equation for the second line. Now recall that the slope of the line is the tangent of an angle this line forms with the x-axis. Indeed, m=(y2-y1)/(x2-x1), where x1, x2, y1, y2 are the x- and y-coordinates of any two distinct points on the line. If one draws the picture, it will be immediately obvious that m is the tangent of the angle between the line and the x-axis. The difference b2-b1 gives the relative displacement along the y-axis of two lines. Since b2 is the y-intercept of the second... read more
Hi All! In the spirit of giving, starting on 11/29/2013, I will be offering a few brainteasers/ trivia questions where the first 3 people to email me the correct answer will receive a free, one hour, tutoring session in any subject that I offer tutoring for (via the online platform)! That's right free! Get your thinking hats on everyone! Merry Christmas!! Andrew L. Profile
1. No one was born to lose. The best of my students understand this principle like the backs of their hands. No, there is no inherent genetic formula or organic compound you can use to get an A in a class. We are all products of our hardwork and investments. Whoever decides to put in excellent work will definitely reap excellent results. 2. Always aim for gold. Have you heard that there is a pot of gold lying somewhere at the end of the rainbow? It's true! Okay, I'm just joking, but my best students always aim for the gold. The very best. As, not Bs, or Cs, or Ds. Just the very best. The one thing people don't think they are capable of achieving is the best. The top of the class. Or the valedictorian. 3. Never settle for less. My best students are innovative, inquisitive thinkers. They tend to think outside the box, never settling for "just what they got from class." They love to use real life examples and explore how theory comes alive in their personal experiences... read more
Area, Volume and Circumference equations: Area of a Square A=S2 Area of a Triangle A=1/2bh Area of a Rectangle A=LW Right Triangle/Pythagorean Theorem a2+b2=c2 Area of Parallelogram A=bh Area of a Trapezoid A=1/2h(a+b) Area of a Circle A=πr2 Circumference of a Circle c=πd or c=2πr Volume of a Sphere V=4/3πr3 Surface Area of a Sphere SA=4πr2 Volume of a Cube V=s3 Volume of a Rectangular Solid V=lwh Slope of a line Equations Slope-intercept form y=mx+b m is the slope b is the y-intercept y is a y coordinate on the graph (that coincides with the line) x is an x coordinate on the graph (that coincides with the line) Horizontal line y=b Vertical line x=a Finding... read more
I have found that many students fear math and business classes as the teacher/instructor knows only a single approach to the topic and additionally cannot show the relevance of the subject with real world examples. With over 20 years of classroom and tutoring experience in math and business topics and my experience in the business and education sectors, I have a huge variety of experiences to draw upon to solve problems and show day-to-day relevance. Learning needs to be fun to engage the student and success must be achieved with every learning situation. I truly enjoy "Turning Distress Into Success"! Larry D.
As the school year ramps up again, I wanted to put out a modified version of a Memo of Understanding http://en.wikipedia.org/wiki/Memo_of_understanding for parents and students. It seems each year in the rush to get through the first weeks of school parents and students forget the basic first good steps and then the spiral downwards occurs and then the need for obtaining a tutor and then the ‘wish for promises’ from a tutor. Pay attention to your child’s folder or agenda book. A student is generally not able to self regulate until well into high school. Some people never quite figure it out. Be the best person you can be by helping your child check for due dates, completeness, work turned in on time. Not only will this help your child learn to create and regulate a schedule, it prevents the following types of conversations I always disliked as a teacher ("Can you just give my child one big assignment to make up for the D/F so they can pass"; "I am going to talk to the principal... read more
I've heard this sentiment over and over--sometimes from students, and sometimes, I'll admit, in my own head. Last night, I was working on my own math homework, and there was one problem I just couldn't get my head around. I read the book, looked back at my class notes, and even sat down with a tutor for a while, and still, when I tried a new problem of the same type on my own, it just didn't work! "Maybe I'm not as good at math as I thought," I told myself. "Am I REALLY smart enough for bioengineering?" It was hard, but I told myself "YES!" And I kept working. I laid the assigned problems aside and started doing other problems of the same type from the book. I checked my work every time. Each problem took at least ten minutes to solve, and the first three were ALL wrong! I kept going. I got one right, and it made sense! I did another, and it was half right, but there was still a problem. I did another, and it was right! Eventually I had a page... read more
Most recently, I was working with a student on the angles in a triangle. We started with a circle to show the angles all the way around, their sizes, and how they compare to each other. Then, I set my arms hand to elbow in an L shape. We worked on showing the sizes of various angles by moving my hand at 12-o'clock (90 degrees) to a position that would show the angle size when my other arm was at 9-o'clock (zero degrees). It worked very well.
I graduated with a BS degree in Chemistry from East Carolina University, Greenville NC. Since then, I worked in pharmaceuticals as a chemist/lab analyst for 1.5 years performing drug analyzes with High Performance Liquid Chromatography, Ultra-Violet Spectrometry, FT-NMR IR, and moisture testing. Also I tutored General Chemistry I and II /Math(pre-algebra, algebra I & II, calculus, geometry at a community college. Also I was a General Chemistry II Lab Instructor at the college and have taken Human Gross Anatomy. If anyone of you need help with Anatomy, let me know! I am a more a visual learner and use concept mapping frequently. I thoroughly enjoy helping students achieve their learning and for them to be able to reach their potential. I look forward in working with you. XX
When interviewing a prospective tutor, parents should ask about the tutor's skills and experience, and find out if the tutor truly enjoys teaching. When the tutor feels enthusiastic about the subject, and communicates well, the student has an opportunity to learn to enjoy the subject too. I recommend for parents to observe the first lesson to see the tutor's skills in action, and watch/listen carefully to future lessons when possible, to make sure the tutor has an encouraging, supportive attitude at all times. (Tutors should welcome and respond positively to the child's questions, and NEVER make the child feel "stupid," no matter what.) It is most important to have a safe and quiet place for studying, without distractions. I like to find a quiet table at a library, and work with students there. I welcome suggestions from parents, and I am always looking for ways to improve my teaching skills.
A few keys to success in school (for people with or without A.D.D.): We need to concentrate on taking notes in classes, and possibly use a digital recorder to record some classes. (That makes a tremendous difference for many of my A.D.D. students, because they can "go back and listen" to things they missed when distractions occurred.) Examples of distractions include when other students are moving or making noises, worries or concerns**, being hungry, needing to go to the restroom, looking for a pen or pencil, or needing to sharpen a pencil, etc. There are many sources of distractions. Even **fear of failure** can be a distraction! What about memory problems? Actually all of us have trouble with remembering from time to time--it's part of being human, right? Heck, even computers have memory problems occasionally, so it seems that some degree of "forgetfulness" is basically a universal condition. Some good news for A.D.D. students: If we are able to use a digital... read more
As you may know, I am a big fan of the well-known author and brain specialist, Dr. Daniel Amen. He mentions in several of his books that Physical Exercise is good for the brain. I have read of research studies that showed a clear correlation between IMPROVEMENT in students' test scores in math and science, and their level of physical activity (for example, when math class followed PE class, the students had significantly higher scores). Maybe we should schedule PE before all math classes in our schools. What do you think about that idea? This morning I read an online article on the myhealthnewsdaily site, entitled "6 Foods That Are Good for Your Brain," and another article about how Physical Exercise helps maintain healthy brain in older adults too. The second article, "For a Healthy Brain, Physical Exercise Trumps Mental Workout" was found under Yahoo News. The remainder of this note is quoted from that article: Regular physical exercise appears to protect the... read more
DEFINITIONS When given two ratios (in the form x:y) or two relations (in the form of fractions), if the ratios of each element are the same they're said to be proportionate. Example: 3/6 and 1/2 are proportionate because 3 out 6 is the same as 1 out of two (half). PROVING PROPORTIONALITY When given two fractions to prove as proportionate, such as 1 and 3 2 6 you solve through cross-multiplication. Cross multiplication involves multiplying the numerator (number on top) by the denominator (number on bottom) of the other fraction, and then comparing the results. If the values are the same, the fractions are proportionate. The set-up above will be set-up as such: 1 * 6 ? 2 * 3 (6) = (6). Because both values are the same, these fractions are proportionate. Example 2: 3/2 and 18/8 The cross-multiplication... read more
Q. Where will we meet for tutoring? A. We will try to find a suitable place that is convenient for both of us. Though I do travel to meet you, time and distance are important factors in making this work feasible and profitable for me, so I try to find locations that minimize my travel time, while also providing convenience to you. Q. How will we decide on a time to meet? A. We will try to find a suitable time that is convenient for both of us. Q. When are you available to tutor? A. It varies from week to week, but my general availability begins at 10:00 a.m., Monday through Saturday, and ends at 9:00 p.m., Monday through Friday, and at 3:00 pm Saturday. Please contact me for my current availability. Q. How long will each session be? A. The session length can vary, depending on the subject, the student, and the schedule. Unless otherwise agreed, the session times will be two (2) hours each. Q. Why do you recommend two (2) hours per session? A.... read more
I was a fairly typical young person and, like my peers, counted down the days until summer. My mother was a math professor, so I never stopped doing math during the summer, but felt like other parts of my brain became a little mushy in the summer. Come September, it was difficult to get back into the swing of writing papers and studying history and memorizing diagrams. I was out of practice and lost my routine. As an adult, I have almost continually taken classes, because I enjoy learning and find that from class to class, I need to maintain a routine, i.e. a study area and a time of day that I complete my assignments. I have also found that reviewing material a week or two before the course begins helps me to start the class with more confidence and competence. I am a big believer in confidence fueling success and I wonder if younger students practiced assignments in the week or two prior to return to school, if that confidence would help the transition to the school year... read more
I was excited on Tuesday, July 16th, 2013. This was my third meeting with this student and I finally had a breakthrough with him. On the first meeting it was clear that he saw Algebra I almost as a foreign language. I began with one of the test packet, and had him do 10 questions and reviewed the questions he had done wrong. So this continued for a while, and of course sometimes he would say that he understood, but it was clear that he did not. Anyway, after reviewing the entire packet I began a teach and learn session, in which I picked a variety of topics and had him practice various equations. After which I gave him a quiz. He failed the quiz miserably, so of course he still did not understand. Anyway, I gave him another packet for homework. When I saw the student again, I reviewed with him, but still not much improvement, but at least he tried. I did the teach and learn session again, of which some of the questions were from the previous session, and I gave him... read more
Although learning is an awesome thing, it can be a difficult and frustrating journey for many students. This difficulty, however, is often times quite normal although most feel it means that a child may not be able to learn or that he/she is so frustrated that learning is no longer taking place. This is where the experienced tutor steps in; for frustration in learning is a part of the learning itself. I have taught and tutored many students and have seen first hand how this frustration can leave some students, and their parents, feeling helpless and hopeless. But there is ALWAYS Hope!!! What they have failed to realize is that as the brain learns difficult concepts, it can only take in parts at a time, little parts at a time. So although it may seem no learning is taking place, it actually is, just in smaller segments. In fact, the most frustration comes right before a new concept is achieved. This is when most give up. Had they stayed focused for perhaps one or two more... read more
Humans have a tremendous capacity to learn and adapt. However, we consistently build barriers that hinder our natural ability to change and grow. Many people, regardless of age, perceive themselves as not being talented enough to excel at math and science. They view math and science as the realms in which only scientists, engineers, mathematicians, and geniuses truly soar. Nothing could be further than the truth. Sure, possessing a natural affinity towards these subjects helps. Yet, a supposed lack of talent does not prevent you from learning. The path may be more arduous. The journey may be longer. Nevertheless, you possess within you the fire to endure. Willpower, dedication, self belief, and an open mind can compensate for any lack of ability. Bruce Lee was a legendary martial artist, actor, and philosopher who continues to inspire millions with the sheer intensity which he pursued his endeavors. Frail, sickly, and small as a child, Bruce Lee overcame many physical... read more