Geometric Krater
The Geometric Krater is a magnificent piece of Greek Art. In the eight century, vase painting became very popular. The vases show a great show a great variety of style and development over the centuries, beginning with the geometric and very linear style. They then continued through the oriental style which borrowed images from the eastern world, and into the classical era with mythology portrayed with as much classical accuracy as the ancient Greek potters and painters could muster. The majority of the vases were made of a ceramic material which could easily be used for everyday uses, however in this time, the artists would then paint on them in order to decorate them and make them ornate enough to be used for cultural or ceremonial uses such as grave markers. The Geometric Krater is a prime example of the vase painting movement in Greek art.

Originally made in approximately 740 B.C in Athens, Greece, the Geometric Krater was used as a grave marker in the Dipylon cemetery and now can be located in the Metropolitan Museum of Art in New York City. The vase stands about three and a half feet high and is in the krater' shape. This shape is classified as having round body, a wide mouth, a heavy stand and a handle on either side, (Pottier). This specific vase was made to serve a purpose besides to decorate the grave site. It was made with holes "cut out of its bottom in order for liquid offerings to be poured to the dead," (Vlamis). The vase itself is golden, embellished with black and red geometric designs. These geometric designs are made up of intense details and intricate designs. The base of the vase is covered in thick black stripes separated by thinner and more decorative golden stripes. On the top half of the vase is where the designs become very intricate and are actually depictions of things. There are two main bands in which scenes are drawn out. Upon looking closely, one will see that the a funeral scene is represented....

...Formal Analysis: Terracotta Krater
The terracotta krater originated in Greece between 750-700 BCE, known as the Geometric period. They were said to have been monumental grave markers. Most kraters were typically large, some over forty inches. They were made of ceramic and painted with linear designs, separated by registers. These vases were used to depict art in order to reveal a story. The artist wanted its viewers to capture the sense of realism in their design.
The designs on the krater demonstrate what is known today as a funeral procession. In the first and widest register, figures surround the elevated body soon to be cremated. The figures closest to the deceased are presumed to be immediate family members and friends. Lined on each side of the body are the mourners. Their bodies are drawn with their arms stretched and hands above their heads, as if they’re pulling out their hair, implicating their sorrow. The figures used in this krater are drawn in geometric shapes (hence the inspiration for the period). Using circles, triangles, and rectangles, the artist conveys their strong presence and nature.
The illustration occupying this krater is clean and precise. The artist was extremely intricate with his drawing, presenting clear lines and shapes. The krater is fully drawn with images, leaving no space on the composition. Artists claimed...

...Assessment 09.08 Geometric Series Activity
Material list:
three different balls of various sizes and textures
measuring tape or yardstick
a blank wall
a step stool or chair
a family member or friend
Procedures:
1. Choose a height from which all of the balls will be dropped one at a time.
2. Vertically along the blank wall, set up the measuring tape and step stool or chair.
3. Have a family member or friend stand on a step stool and drop one of the balls from the chosen height away from the measuring tape.
4. Face the measuring tape, opposite the ball’s starting point from about 7 or 8 feet. As the ball falls, measure the height of the ball on four consecutive bounces. (You may need to repeat the process to ensure that your measurements are accurate. You may choose to video each drop to assure accuracy.)
5. Write the height of each bounce, beginning with the height from which the ball originally fell,
in the chart below.
Ball 1
Description:
Ball 2
Description:
Ball 3
Description:
Height 1
(starting point)
Height 2
Height 3
Height 4
Height 5
6. Repeat the process with each ball. Be sure that each ball is originally dropped from the same height.
7. Beginning with Height 1, plot the height number (1, 2, 3, …) on the x-axis and the corresponding height measurement on the y-axis in GeoGebra. You may do this by using the New Point icon in the toolbar or by typing each ordered pair in the Input bar.
Be sure that you can see...

...CHAPTER 7 ARITHMETIC AND GEOMETRIC PROGRESSIONS
7.1 Arithmetic Progression (A.P)
7.1.1 Definition
The nth term of an arithmetic progression is given by
,
where a is the first term and d the common difference. The nth term is also known as the general term, as it is a function of n.
7.1.2 The General Term (common difference)
Example 7-1
In the following arithmetic progressions
a. 2, 5, 8, 11, ...
b. 10, 8, 6, 4, ...
Write (i) the first term, (ii) the common difference,
(iii) (iv)
Solution i) a. 2 b. 10
ii) a. 5-2 = 3 b. 10 -8 = 2
iii) a. = 14
b. = 2
iv) a. = 59
b. = 48
Example 7-2
How many terms are there in the following arithmetic progression?
(i) 3, 7, 11, 15, ... , 79. (ii)
Solution i)
ii)
7.1.3 The sum of the First n-Terms
or
Example 7-3
a. Find the sum of 20 terms of the following arithmetic progression:
(i) 1 + 2 + 3 + 4 + ... (ii) 5 + 1 + (3) + (7) + ...
Solution (i)
(ii)
b. Find the sum of the following arithmetic progression:
(i) 13 + 17 + 21 + ... + 49. (ii) 2.3 + 2.7 + 3.1 + ... + 9.9.
Solution (i)
(ii)
7.1.4 Solving Questions on Arithmetic Progression
The questions on arithmetic progression usually involve
(i) a term and another term,
(ii) a term and a sum,
(iii) a sum and another sum,
(iv) the definition of arithmetic progression.
(v)
Example 7-4
The third term of an arithmetic progression is 14 and the sixth term is 29....

...
This work MAT 126 Week 1 Assignment - Geometric and Arithmetic Sequence shows "Survey of Mathematical Methods" and contains solutions on the following problems:
First Problem: question 35 page 230
Second Problem: question 37 page 230
Mathematics - General Mathematics
Week One Written Assignment
Following completion of your readings, complete exercises 35 and 37 in the “Real World Applications” section on page 280 of Mathematics in Our World .
For each exercise, specify whether it involves an arithmetic sequence or a geometric sequence and use the proper formulas where applicable . Format your math work as shown in the Week One Assignment Guide and be concise in your reasoning. Plan the logic necessary to complete the exercise before you begin writing. For an example of the math required for this assignment, please review the Week One Assignment Guide .
The assignment must include ( a ) all math work required to answer the problems as well as ( b ) introduction and conclusion paragraphs.
Your introduction should include three to five sentences of general information about the topic at hand.
The body must contain a restatement of the problems and all math work, including the steps and formulas used to solve the problems.
Your conclusion must comprise a summary of the problems and the reason you selected a particular method to solve them. It would also be appropriate to include a...

...Lesson Plan
Name: Geometric Solids
Content Area: Math
Grade Level: Kindergarten
Time Frame: 45 min
Prior to this lesson the students had a lesson on attributes. The children defined and identified attributes in different two-dimensional shapes.
MA Framework Standard:
Geometry K.G
Identify and describe shapes (squares, circles, triangles, rectangles, hexagons, cubes, cones, cylinders, and spheres).
2. Correctly name shapes regardless of their orientations or overall size. Identify shapes as two-dimensional (lying in a plane, “flat”) or three-dimensional (“solid”).
Student Learning Objective:
CONTENT OBJECTIVE: Student will be able to identify the following geometric solids: cube, sphere, cylinder, and cone.
LANGUAGE OBJECTIVE: Student will use the following terms when identifying geometric solids: cube, sphere, cylinder, and cone.
Interdisciplinary content area: Language
Materials necessary for today’s lesson:
For Students: For Teacher
Colored Pencils or crayons -Geometric solids
Pencil -Cube, sphere, cylinder, cone
Enough sets for each group of four students to have a complete set
-Pictures of cubes, spheres, cylinders, and cones.
-Tally sheet one for each group
-Worksheet one per student
Academic Vocabulary:
Cube, sphere, cylinder cone, attribute, geometric solid, three-dimensional...

...1
“Arithmetic vs. Geometric Means: Empirical
Evidence and Theoretical Issues”
by Jay B. Abrams, ASA, CPA, MBA
Copyright 1996
There has been a flurry of articles about the relative merits of using the arithmetic mean
(AM) versus the geometric mean (GM). The Ibbotson SBBI Yearbook took the first position
that the arithmetic mean is the correct mean to use in valuation. Allyn Joyce’s June 1995
BVR article initiated arguments for the GM as the correct mean.
The previous articles have centered around Professor Ibbotson’s famous example using a
binomial distribution with 50%-50% probabilities of a +30% and -10% return. The debate
has been very interesting, but it is off on a tangent, focused on the wrong issue.
There are theoretical and empirical reasons why the arithmetic mean is the correct one.
We will look at both in this article.
Theoretical Superiority of Arithmetic Mean
Rather than argue about Ibbotson’s much debated above example, I prefer to cite and
elucidate another quote from his book:
In general, the geometric mean for any time period is less than or equal to
the arithmetic mean. The two means are equal only for a return series that
is constant (i.e., the same return in every period). For a non-constant
series, the difference between the two is positively related to the variability
or standard deviation of the returns. For example, in Table 6-7, the
difference between the arithmetic and...

...Sums
Introduction
A geometric sequence is a sequence such that any element after the first is obtained by multiplying the preceding element by a constant called the common ratio which is denoted by r. The common ratio (r) is obtained by dividing any term by the preceding term, i.e.,
where | r | common ratio |
| a1 | first term |
| a2 | second term |
| a3 | third term |
| an-1 | the term before the n th term |
| an | the n th term |
The geometric sequence is sometimes called the geometric progression or GP, for short.
For example, the sequence 1, 3, 9, 27, 81 is a geometric sequence. Note that after the first term, the next term is obtained by multiplying the preceding element by 3.
The geometric sequence has its sequence formation:
To find the nth term of a geometric sequence we use the formula:
where | r | common ratio |
| a1 | first term |
| an-1 | the term before the n th term |
| n | number of terms |
Sum of Terms in a Geometric Progression
Finding the sum of terms in a geometric progression is easily obtained by applying the formulas:
nth partial sum of a geometric sequence
sum to infinity
where | Sn | sum of GP with n terms |
| S∞ | sum of GP with infinitely many terms |
| a1 | the first term |
| r | common ratio |
| n | number of terms |
Examples of Common Problems...

...1. What is the sum of the geometric sequence 8, –16, 32 … if there are 15 terms? (1 point)
= 8 [(-2)^15 -1] / [(-2)-1]
= 87384
2. What is the sum of the geometric sequence 4, 12, 36 … if there are 9 terms? (1 point)
= 4(3^9 - 1)/(3 - 1)
= 39364
3. What is the sum of a 6-term geometric sequence if the first term is 11, the last term is –11,264 and the common ratio is –4? (1 point)
= -11 (1-(-4^n))/(1-(-4))
= 11(1-(-11264/11))/(1-(-4))
= 2255
4. What is the sum of an 8-term geometric sequence if the first term is 10 and the last term is
781,250? (1 point)
=8 (1-390625)/(1-5)
=781,248
For problems 5 8, determine whether the problem should be solved using the formula for an arithmetic sequence, arithmetic series, geometric sequence, or geometric series. Explain your answer in complete sentences. You do not need to solve.
5. Jackie deposited $5 into a checking account in February. For each month following, the deposit
amount was doubled. How much money was deposited in the checking account in the month of August? (1 point)
To solve this, a geometric sequence is used because the terms share a constant ratio as 2.
6. A local grocery store stacks the soup cans in such a way that each row has 2 fewer cans than
the row below it. If there are 32 cans on the bottom row, how many total cans are on the bottom 14 rows? (1 point)
To solve you...