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The Original Charleston Math Trail #9 21 East Battery - Edmonston-Alston House Charles Edmonston was a Scotsman who made his fortune as a merchant. He had this house built circa 1829 on the site of one of Charleston's first defenses, Fort Mechanic. This fort was built in 1795 by the mechanics of Charleston. Carpenters and other artisans worked free of charge to protect the young nation. The house was sold in 1839 to satisfy debts totaling $125,000 to Charles Alston. This distinguished family included Theodosia Burr Alston, Aaron Burr's daughter, who was the wife of South Carolina's governor. Sadly, she was lost at sea. Today, the Historic Charleston Foundation operates the main house as a museum. 1. Let n = the number of floors of the house, evaluate: (n −2 1) (2n – 1) + n. 2. Let n = the number of windows on the first floor facing East Battery. Evaluate the

complex number: 40 – 3in.

windows

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East Bay - Home of the bride of “Mad Archie Campbell” This house (c. 1755) stands on part of Lot No. 1 of the Grand Modell, which was granted to Maurice Matthews and James Moore by the Lord Proprietors in 1682. It was owned by George Sommers and remained in the Sommers’ family until the 1790s. The bend in East Bay where it connects to East Battery was also known as “Sommer’s Corner”. Another interesting story about this house is that one of its inhabitants has a ghost tale. Miss Paulina (Polly) Phelps was the girlfriend of Captain Archie Campbell (Mad Archie Campbell). Archie had made a wager that he would marry Polly with her consent in three days or lose his Arabian Philly. He arrived at her home to take her on an afternoon ride in the country. When they arrived at the Goose Creek Church and told the minister at gunpoint to marry them or be shot. The minister asked if the lady consented and Archie pointed the gun at his Paulina as he said “the lady does consent” and she said “yes.” They were very happy together living on Exeter Plantation, but for only a short time for Archie was killed and Paulina died shortly afterwards. The ghost tale says that Paulina returns to Exeter in search of their baby she left behind. 1. Let n = the year that Lot No. 1 was granted to Maurice Matthews and James Moore

by the Lord Proprietors. Evaluate: n - 40 2 - 3 x 7 2. Let [ ]A be a 2x2 matrix with the following entries that refer to the East Battery

facade of the house. Find the determinant of the matrix.

windowsfloor1stonshutters#7

2houseinfloors#windowfloor1stoneinpanes# +

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Church Street - First Baptist Church The First Baptist Church, the oldest Baptist church in the South, is called the "Mother Church” of Southern Baptists. Organized in Kittery, Maine, this church was driven by persecution to South Carolina in 1683. In 1699, William Elliot donated the present lot on Church Street and a frame building was erected. The cornerstone of the present church was laid in September 1819. It was designed by architect Robert Mills, who considered it "the best specimen of correct taste in architecture of all the modern buildings in this city." Although Mills said the building was "purely Greek in its style," it actually has Tuscan columns and Roman arches. Mills may also have designed the iron gates and fence, which are of Guilloche design of alternating curves and lozenges. 1. Let n = the sum of the degrees of the semicircular windows above the doors facing

the street. Evaluate: 510

+n

2. Approximate the circumference of the arch above one of the semicircular windows at

the entrance to the church, using 722 for π and assume the diameter of the arch is 7

feet. Evaluate: 6(circumference of this semicircle - 1) + cos(# of degrees in a semicircle)

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Church Street – Ladd Brown House (also Thomas Rose House) Thomas Rose, an Ashley River planter, is said to have built this two and one-half story stuccoed brick house soon after his marriage to Beuler Elliot in 1733. The house has an asymmetrical plan typical of early Charleston houses, and early Georgian interiors with robust and simple paneling, staircase and other woodwork. The piazza is a 20th century addition. The house is said to be haunted by the ghost of Dr. Joseph Ladd Brown, who in 1786 was carried into the house after being mortally wounded in a duel, in which he defended the honor of an actress named "Mrs. Robertson," nicknamed "Perdita." 1. Begin with the year Dr. Brown was mortally wounded at this house, subtract the house

number, subtract 1700, multiply by 3, and then subtract 10. 2. A “piazza” is a large porch or veranda. Find the number of arrangements of the letters

in the word “piazza”. Take this result, divide it by three, and then add eleven.

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Church Street - Colonel Robert Brewton House The spirited woman who once owned this house, Mary Weyman Brewton Foster, talked back to a British officer, Lt. Col. Banastie Tarleton, and was banished to Philadelphia for her nimble wit and sharp tongue. The lieutenant colonel said, "I would like to see this fellow Washington of whom people talk so much." Whereupon Mrs. Foster retorted: "What a pity you did not look behind you at the Battle of Cowpens." The house is one of Charleston's earliest examples of a single house. 1. Let n = the number of windows facing the street. Evaluate: 900% of n + 50% of n. 2. The wrought iron balcony of the house encloses a small area that looks like the

drawing below. Assume the following measurements: radius of the semicircle = 2 feet, length of the rectangular region = 8 feet, and width of the rectangular region = 3 feet. Evaluate: 3[cos(area of semicircle) + area of rectangular region] + 1

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Church Street - DuBose Heyward House In this small, notable post-Revolutionary house, DuBose Heyward wrote Porgy, the novel on which the operetta Porgy and Bess was based. It was designated a National Historic Landmark in 1972. The house has been combined with 78 Church Street, another post-Revolutionary dwelling, into one residence. Tradition says President George Washington spoke from a balcony at 78 Church Street on his visit to Charleston in 1791. The present balcony, however, is in the Regency style of c. 1815-25. The third floor of 78 Church Street is partly supported by a mahogany bedpost. 1. DuBose Heyward wrote the novel Porgy at this house. Assigning each letter of the

alphabet to a number, beginning with A = 1, B = 2, etc., determine the sum of the letters in the title Porgy and then add six.

2. Refer to the title of the operetta written by Gershwin that was based on the novel

written by DuBose Heyward. Determine the probability that a letter chosen at random from this operetta title will be a vowel (not including y). Let this result represent the

number n. Evaluate the expression 2

5 2 1n n

+ −

.

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Church Street - Heyward Washington House Daniel Heyward, a rice planter and founder of a prominent rice-planting dynasty, built this brick double house in 1772. He removed a two-story brick house from the site but may have kept the existing outbuildings. The house was the home of his son Thomas Heyward, a signer of the Declaration of Independence. President George Washington stayed here on his visit to the city in 1791. During the late 19th century, the lower left corner of the house was converted to a bakery. The house was restored in 1929 by the Charleston Museum and the Preservation Society of Charleston and is operated as a house museum by the Garden Club of Charleston.

1. Let n = the number of red brick steps at doorway. Evaluate: n +3 n 2 + n – 5.

2. Evaluate the sum of the sequence defined by1(8 1)

n

kk

=

−∑ , where n = the number of

windows on the first floor façade on Church St. Add three to this sum.

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East Bay - Rainbow Row "Rainbow Row" is a name coined in the 1930s because these homes were painted in a variety of pastel colors. From a slum to a highly sought after neighborhood, these houses were gradually changed, beginning in the 1920s and '30s. Built as merchant's houses, some as early as 1740, the buildings originally had stores and counting houses on the first level and residences above.

1. Let n = the first year of the decade in which the name was coined and let m = the year

the earliest house was built. Evaluate: 3

14)(2 −−mn

2. A rainbow is sometimes called the “circle of light”. Find the y-coordinate of the

center of the circle whose equation is ( )22( 3) 122 36x y− + − = .

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East Bay - Old Exchange The Old Exchange and Custom House was built in 1767-71. William Rigby Naylor was the architect of the building that was constructed by the brothers Peter and John Adam Horlbeck. The building is reminiscent of exchanges in London, Liverpool, and Bristol. It originally had an open arcade on the first floor and an elegant assembly on the second. Twin stair towers, which projected into East Bay Street, were taken down in the early part of the 19th century. The building was conveyed to the Federal government in 1818 and became the Post Office. In 1912, the Rebecca Motte Chapter of the Daughters of the American Revolution began negotiating to acquire the property but did not occupy it until 1921. In 1972 restoration of the Exchange Building began at a cost $1,910,000. The restoration is a modern adaptation of the historic building and is not meant to be an exact replication of the original appearance. The stair towers for example, were replaced, not on the west front where they would again have impeded traffic, but on the east side.

1. Let N = the sum of the degrees of the 3 rectangular windows. Let M = the sum of the angle measures of the 3 semicircular windows. What percent of M is N?

2. Above the entrance to the Exchange building is a window consisting of three

concentric semicircles. Find the central angle in one of the sectors for the innermost semicircle and let this value be your value forθ . Evaluate the expression: 22 tan 10θ ⋅ .

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East Bay Street at Market Street - Custom House With funds appropriated by Congress in 1848, the site of Fitzsimons’ Wharf was bought in 1849 to build the US Custom House. During excavation of the basement, the remains of Craven’s Bastion, a colonial-era fortification, were found. The building’s construction, interrupted by the Civil War, was completed in 1879 as it is today. Marble was used for the two upper floors. Roman Corinthian porticos, engaged columns, and entablature (the section that lies between the columns and the roof) surround the cruciform (shaped like a cross) building. Emile T. Viett carved the marble capitals and decorative work. Congratulations! You have completed your Math Trail. We hope that you were able to

work the problems, learn some history and most of all had fun doing math with friends.