If Ahmed used string and tied it to the Castle Rock point and labeled it as point “A” on paper it would be basically 2x + 6 paces. With this being the radius you will know that it is the same anyway you fit this from the circle. So to find the Treasure we will use “C”. Vanessa will use her compass to find north from Castle Rock. From there she will walk “X” paces in a straight line northward. At the end of her distance she will call this point “B”. Vanessa will now turn 90 degrees to the right and will walk 2x+4 paces east until she is at point “C”. We have now acquired a line segment which we will call AB which is basically the line from A to B, the line segment from B to C is considered BC. However, the lines AB and BC intersect to form a perpendicular angel, and we will use line AC as Ahmed’s route. The end state of the line segments if one was to draw them out would equal a triangle. With the face that Vanessa had turned in a 90 degree angle that makes this triangle a right angle ABC. Lines AB and BC are to be considered as the legs and we will think of AC as the…
from the gods” and had stayed up pondering his options. Why would he have come to my house and arranged triangles from firewood? “It’s nothing.” I said quickly. “And it’s not a book. I can’t read.” That was a lie, I could read very well. “Go home. Why are you at my house anyways?” “Don’t burn the book.” Pythagoras warned me, and I got the message that he had seen it. “Daphne, when you’re done with…
At about twenty centuries ago there was an amazing discovery about right angled triangles: “In a right angled triangle the square of the hypotenuse is equal to the sum of squares of the other two sides.” It is called Pythagoras Theorem and can be written in one short equation: a²+b²=c² where c is the longest side of triangle and a and b are the other two sides. Pythagoras was born in the island of Samos in 570 BC in Greek in the eastern Agean. He was the son of Mnesarchus and his mother's name…
the activity applies to Van Hiele’s level 1 which is the Visual Level because the children have to identify what shapes were used in the Ozella quilt. For example, “the students should be able to know that four squares are together to make crossroads or that squares and right triangle was used to a Bear’s Claw.” This concept applies to Van Hiele’s Level 2 which is the Descriptive and Relational level. In this level, the students will recognize or analyze figures by their properties or…
tree sides of a right triangle. It’s the sum of the areas of the two squares on the legs equals the area of the square on the hypotenuse. The equation use for it is A squared plus B squared equals C squared.The Theorem relates the lengths of the three sides of any right triangle. The theorem is named after the ancient Greek. There is evidence that indicates that Pythagorean Theorem was well- known to the mathematicians of the first Babylonian Dynasty (20th to 16th centuries BC) which would…
based learning activity for my student’s. How does it connect art with another discipline: My fourth graders have been learning about the Six Pillars of Characters and what each pillar stands for. The Six Pillars of Characters are Trustworthiness, Respect, Responsibility, Fairness, Caring, and Citizenship.(The Six) As a fun way for the students to show me what they have learned about the six different pillars, I will be incorporating role play into their final lesson on the Six Pillars of…
THE SINE FUNCTION (SIN) Sine function is an odd function. Trigonometric Ratios in a Triangle Definition of sinα in a Triangle is the following statement: For any acute angle α, we draw a right triangle that includes α. The sine of α, abbreviated sin α, is the ratio of the length of the opposite this angle to the length of the hypotenuse of the triangle. If we simplify we get a formula which says: It is shown in a diagram below. We can see immediately that this definition has a weak point. It…
At first, as I was examining the image of the swimmer, I thought about determining the area between the swimmer’s legs. At first, I thought that I could relate it to the area of a triangle, but later acquired the fact that the side length and height of an isosceles triangle cannot be equivalent, which meant that the area of a triangle would not fit this image. Figure 2 Created in Microsoft Paint In Figure 2, I have attempted to display an isosceles triangle to put in place of the swimmer's…
School to develop our wide spectrum of ideas and abilities into a highly sophisticated product. While the studies at Governor’s School are noticeably more advanced and require more effort than at regular public schools, I see this rigor as the key to my academic success. For me, the classes I take that constantly introduce new thoughts that test my capability to “think outside the box”, are the ones that capture all my attention and interest. For example, while working with the Sierpinski…
Circumradius and Inradius of a non-degenerate triangle then due to Euler we have an Inequality stated as and the equality holds when the triangle is equilateral. This ubiquitous inequality occurs in the literature in many different equivalent forms [4] and also Many other different simple approaches for proving this inequality are known. (some of them can be found in [2], [3], [5], [17], and [18] ). In this article we present a proof for this Inequality based on two basic lemmas, one is on the…