Share
Explore BrainMass

Geometry and Topology

Geometric constructions

USING ONLY AN UNMARKED STRAIGHT EDGE AND A COMPASS CONSTRUCT THE FOLLOWING: (A) A RHOMBUS GIVEN: ONE SIDE AND ONE ANGLE (B) A PARALLELOGRAM GIVEN: TWO ADJACENT SIDES AND THE INCLUDED ANGLE (C) A PARALELLOGRAM GIVEN: THE DIAGONALS AND THE ANGLE BETWEEN THEM ********I NEED STEP-BY-STEP INSTRUCTIONS ON HOW TO CONSTRUCT

Proving a Set E is Compact

Please see the attached file for the fully formatted problems. Let lambda n be a real decreasing sequence converging to Prove E is compact if and only if = 0. I am assuming compactness here refers to the sequential compactness. This seems to make the most sense. Since this problem is an analysis problem, please be

Construct a geometric model using axioms

Construct a model that satisfies the following axioms. - 1. There exists at least 1 line. - 2. Every line of the geometry has exactly 4 points on it. - 3. Not all points of the geometry are on the same line. - 4. Each point of the geometry is contained in exactly 3 lines. - 5. Every pair of lines intersect and their interse

Maximum volume

Find the maximum possible volume of a rectangular box if the sum of the lengths of its 12 edges is 6 meters.

Transformation Geometry Proofs : Reflections

Please see the attached file for the fully formatted problems. Let l, m, n be distinct lines and P, Q, R be distinct points. Prove the following: (a) sigma l sigma m = sigma m sigma l if and only if l perpendicular to m. (b) sigma p sigma m = sigma m sigma p if and only if P E m. plus three more questions

Creating the formula to find the dimensions of a cube.

In Metric. Three college students are trapped in deep snow in northern Canada. To survive they must build an igloo using snow large enough for all of them to fit and small enough to not exceed their strength and stamina. Luckily one of them is a math major and quickly formulates the dimensions of the blocks they need to cu

Comparing Areas

Calculate AREA of Shape 1 then calculate the area of Re-arranged Shape 1. Did you get the same result? Why are they different? Please see the attached document.

Measurement of a parallelepiped brick's diagonal

You have a brick of parallelepiped shape. You need to measure its diagonal (a distance between two opposite vertexes remote to the maximum). You have in your disposition a ruler and a rectangular edge of the plane surface (of the table, for example). What should you do to measure the diagonal if 1. You have also a pencil to ma

Geometry: Angles

Suppose <ABC and<CBD form a linear pair, <CBD and <DBE form a linear pair, and m<CBD=30. A. Draw a figure representing these angles. B. Write a paragraph proof showing that <ABC=<DBE.

Rigid Pentagonal Prism

How many lines would you need to add to a pentagonal prism anchored to the ground to make it rigid?

Calculating the departure angles.

For a gun where the departure angle 'Beta' and the distance "D" in meters that the projectile travels are related by D=1250sin2Beta. Find which departure angles can be used to hit a target 800 meters away.

Finding Apothems

Please explain how to find the apothem, especially in regards to 45-45-90 and 30-60-90 triangles.

Symbols

What is this symbol and what does it mean? See attachment.

Proving that h meets line AD.

Assume that AC < w, A-B-C, and D is a point on AC line segment. Let h be a ray with endpoint C such that h meets BD line interior. Prove that h meets AD line.