Construct altitude geometry7/30/2023 ![]() ![]() ![]() ![]() I do not understand trigonometry very well because I am not very well educated, but this is Euclid's approach to the problem which is general for generating similar figures of any kind of a given area, which, although perhaps cumbersome, I found convenient and readily intelligible.Īn equilateral triangle is made, a parallelogram constructed equal to it, another equal to the desired area applied alongside it in the parallels, then a mean proportional taken between the lengths of the two parallelograms. Thank you to all you brilliant mathematicians for your ingenious methods on this topic. Then draw the parallel to AB through H and intersect it with AD (at point K) to cut off the correct side length (AK) of equilateral triangle. The construction of the geometric mean is made easier by extending line CD to E so that P is the midpoint of EC, then using ED as diameter of a circle and taking $g=|PG|$ for PG a perpendicular to CD with G on the circle. The equilateral triangle whose "height" measured along line PCD (from P) is $g$ has the same area as the given triangle. Find a length $g$ equal to the geometric mean of PC and PD, and take a point H on PD with PH = $g$. On one of the sides, say AB, build an equilateral triangle ABD. The savings is in re-using one side of ABC as the base of the equilateral triangle, and in using a non-perpendicular line to measure altitude, and allowing the semicircle construction of geometric mean to be applied. Here is a relatively efficient construction using a geometric mean. Something like a geometric mean is unavoidable since the problem is a quadratic equation for the side length of the equilateral triangle. Short reviews of the various science resources and curricula I have used with my own children.The fewer steps the better I found I had to use the geometric mean construction and I wonder whether this step might be avoidable. Keeping math skills sharp in the summer.Mental math "mathemagic" with Arthur Benjamin (video).Seven reasons behind math anxiety and how to prevent it.This article explains some of those relationships. ![]() To do that, they need to see the RELATIONSHIP between the different quantities in the problem. Students often have problems setting up an equation for a word problem in algebra. How to set up algebraic equations to match word problems.The do's and don'ts of teaching problem solving in mathĪdvice on how you can teach problem solving in elementary, middle, and high school math.Hint: it has to do with a "recipe" that many math lessons follow. Why are math word problems SO difficult for children?.Four habits of highly effective math teaching.How to calculate a percentage of a number.Multiply and divide decimals by 10, 100, and 1000.Dividing fractions: fitting the divisor.Adding unlike fractions 2: Finding the common denominator.Multiplication Algorithm - Two-Digit Multiplier.Structured drill for multiplication tables.Multiplication concept as repeated addition.Add a 2-digit number and a single-digit number mentally.Fact families & basic addition/subtraction facts.Using a 100-bead abacus in elementary math. ![]()
0 Comments
Leave a Reply.AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |