Good morning.

We’ll have a partly sunny Wednesday in Whitewater, with a high of eighty, and southwest winds at 5 to 15 MPH.

I had no idea that Pres. Garfield had an interest in mathematics, but yesterday I learned that he did. While a member of Congress, he produced a simple proof of the Pythagorean theorem, as Esther Inglis-Arkell explains:

Most will remember the Pythagorean Theorem as the old A² + B² = C² problem, wherein the square of the two sides of a right triangle, added together, will yield the square of the hypotenuse. Garfield’s proof is simple, but it takes a little fiddling with paper.

Grab a piece of paper and cut two identical right triangles, trying to include one long side and one short side. Call the long side A, the short side, B, and the hypotenuse C. Place them, opposing points together, on a piece of paper so that they look like this.

Draw the third line in and you’ve made three triangles. The total area of a triangle can be calculated as one half the base times the height. Each of the original triangles has an area of ½ ab, and the third has an area of ½c².

A trapezoid has an area calculated by its height times one half the sum of its uneven sides. So the trapezoid has an area of ½ (a+b)(a +b).

Since these areas are the same, this leads us to an equation.

½ ab + ½ ab + ½c² = ½ (a + b)(a +b)

This simplifies quickly. On the left, the two halves of ‘ab’ can be added together. On the right, we just multiply all the terms.

ab +½c² = ½ (a² + b² + 2ab)

ab +½c2 = ½ a² + ½ b² + ab

Since we have ‘ab’ on either side, they cancel each other out.

½c² = ½ a² + ½ b²

Multiply it all by 2, and you get:

c² = a² + b²

Well, you get that, and the deep satisfaction that you have solved a problem, Presidential-style.

From mathematics to a different sort of puzzle:

Puzzability‘s series this week is about mythology:

Myth Takes
For this week of freaks and Greeks, we started each day with a mythical creature. Then we hid it in a sentence, with spaces added as necessary. The answer spans at least two words in the sentence and starts and ends in the middle of words. The day’s clue gives the sentence with a Greek column in place of the creature.

Example:
I am not rising from this comfortable sotil I’ve finished this fascinating myth about the early days of Mt. Olympus.

Answer:
Faun (sofa until)

What to Submit:
Submit the mythical creature (as “Faun” in the example) for your answer.

Wednesday, August 7:

In Roman mythology, the iridesora (the goddess Eos in Greek myths) creates a beautiful dawn across the sky.

Good morning.

We’ll have a partly sunny day with a high of eighty-three.

Common Council meets today at 6:30 PM.

On this day in 1945, fewer than fours years after the Japanese attack on Pearl Harbor, America bombs Hiroshima:

…at 8:16 a.m. Japanese time, an American B-29 bomber, the Enola Gay, drops the world’s first atom bomb, over the city of Hiroshima. Approximately 80,000 people are killed as a direct result of the blast, and another 35,000 are injured. At least another 60,000 would be dead by the end of the year from the effects of the fallout.

U.S. President Harry S. Truman, discouraged by the Japanese response to the Potsdam Conference’s demand for unconditional surrender, made the decision to use the atom bomb to end the war in order to prevent what he predicted would be a much greater loss of life were the United States to invade the Japanese mainland. And so on August 5, while a “conventional” bombing of Japan was underway, “Little Boy,” (the nickname for one of two atom bombs available for use against Japan), was loaded onto Lt. Col. Paul W. Tibbets’ plane on Tinian Island in the Marianas. Tibbets’ B-29, named the Enola Gay after his mother, left the island at 2:45 a.m. on August 6. Five and a half hours later, “Little Boy” was dropped, exploding 1,900 feet over a hospital and unleashing the equivalent of 12,500 tons of TNT. The bomb had several inscriptions scribbled on its shell, one of which read “Greetings to the Emperor from the men of the Indianapolis” (the ship that transported the bomb to the Marianas).

Puzzability‘s new series this week is about mythology:

Myth Takes
For this week of freaks and Greeks, we started each day with a mythical creature. Then we hid it in a sentence, with spaces added as necessary. The answer spans at least two words in the sentence and starts and ends in the middle of words. The day’s clue gives the sentence with a Greek column in place of the creature.

Example:
I am not rising from this comfortable sotil I’ve finished this fascinating myth about the early days of Mt. Olympus.

Answer:
Faun (sofa until)

What to Submit:
Submit the mythical creature (as “Faun” in the example) for your answer.

Tuesday, August 6:

The preacmas of Euripides are a bit much for me; I prefer lightweight comedies by playwrights like Aristophanes.

Good morning.

Whitewater will have a Monday of showers with a high of seventy-one.

The School Board meets tonight, first in closed session at 6 PM and later to open session.

On this day in 1914, a new method of traffic regulation:

The world’s first electric traffic signal is put into place on the corner of Euclid Avenue and East 105th Street in Cleveland, Ohio, on this day in 1914….

Various competing claims exist as to who was responsible for the world’s first traffic signal. A device installed in London in 1868 featured two semaphore arms that extended horizontally to signal “stop” and at a 45-degree angle to signal “caution.” In 1912, a Salt Lake City, Utah, police officer named Lester Wire mounted a handmade wooden box with colored red and green lights on a pole, with the wires attached to overhead trolley and light wires. Most prominently, the inventor Garrett Morgan has been given credit for having invented the traffic signal based on his T-shaped design, patented in 1923 and later reportedly sold to General Electric.

Despite Morgan’s greater visibility, the system installed in Cleveland on August 5, 1914, is widely regarded as the first electric traffic signal. Based on a design by James Hoge, who received U.S. patent 1,251,666 for his “Municipal Traffic Control System” in 1918, it consisted of four pairs of red and green lights that served as stop-go indicators, each mounted on a corner post. Wired to a manually operated switch inside a control booth, the system was configured so that conflicting signals were impossible. According to an article in The Motorist, published by the Cleveland Automobile Club in August 1914: “This system is, perhaps, destined to revolutionize the handling of traffic in congested city streets and should be seriously considered by traffic committees for general adoption.”

On this day in 1850, Wisconsin gets a new fraternal organization:

1850 – Order of the Druids Organized in Milwaukee
On this date the Order of the Druids was organized in Milwaukee. One of the oldest fraternal organizations in Wisconsin, Wisconsin Grove No. 1 was organized by charter members A.F. Hausemann, H.M. Brietz, Joseph Lachner, and G.F. Becker. The order offered benefits and insurance for its members. [Source: History of Milwaukee, Vol.II, by William George Bruce, p.285]

Puzzability‘s new series this week is about mythology:

Myth Takes
For this week of freaks and Greeks, we started each day with a mythical creature. Then we hid it in a sentence, with spaces added as necessary. The answer spans at least two words in the sentence and starts and ends in the middle of words. The day’s clue gives the sentence with a Greek column in place of the creature.

Example:
I am not rising from this comfortable sotil I’ve finished this fascinating myth about the early days of Mt. Olympus.

Answer:
Faun (sofa until)

What to Submit:
Submit the mythical creature (as “Faun” in the example) for your answer.

Monday, August 5:

Some people called Zeuant, but many mortals felt he was a benevolent ruler.

Good morning.

We’ll have a mostly sunny day in Whitewater, with a high of seventy-five.

NASA’s Jet Propulsion Laboratory offers a video if the Mars Curiosity lander’s first year on that planet, distilled into two minutes’ time:

On this day in 1753, George Washington advances in Freemasonry:

…21-year-old Virginian George Washington is declared a Master Mason in a Masonic ritual performed by his fellow Freemasons during a secret ceremony in Fredericksburg, Virginia. Washington, who belonged to Alexandria Lodge No. 22, had been initiated into the Masons at age 20 on November 4, 1752. The following year, on March 3, 1753, he passed as a “Fellow Craft.” Five months later, Washington was raised to the rank of Master Mason.

On August 4, 1862, Wisconsin sees riots against a federal order:

1862 – War Department Order Prompts Riot
On this date the War Department issued General Order No.99, requesting by draft 300,000 troops to reinforce the Union armies in the Civil War. This action reinforced public sentiment against the draft and prompted the citizens in Port Washington, Ozaukee County to riot in protest.

Good morning.

Whitewater will have a sunny Saturday, with a high of seventy-six and northwest winds at 5 to 10 MPH.

On this day in 1958, a remarkable vessel takes a remarkable trip:

On August 3, 1958, the U.S. nuclear submarine Nautilus accomplishes the first undersea voyage to the geographic North Pole. The world’s first nuclear submarine, the Nautilus dived at Point Barrow, Alaska, and traveled nearly 1,000 miles under the Arctic ice cap to reach the top of the world. It then steamed on to Iceland, pioneering a new and shorter route from the Pacific to the Atlantic and Europe.

The USS Nautilus was constructed under the direction of U.S. Navy Captain Hyman G. Rickover, a brilliant Russian-born engineer who joined the U.S. atomic program in 1946. In 1947, he was put in charge of the navy’s nuclear-propulsion program and began work on an atomic submarine. Regarded as a fanatic by his detractors, Rickover succeeded in developing and delivering the world’s first nuclear submarine years ahead of schedule. In 1952, the Nautilus’ keel was laid by President Harry S. Truman, and on January 21, 1954, first lady Mamie Eisenhower broke a bottle of champagne across its bow as it was launched into the Thames River at Groton, Connecticut. Commissioned on September 30, 1954, it first ran under nuclear power on the morning of January 17, 1955.