Neil’s words from the last episode of “Cosmos: A Spacetime Odyssey”
This animation is about one of the most significant problems in the history of mathematics: the brachistochrone challenge.
If a ball is to roll down a ramp which connects two points, what must be the shape of the ramp’s curve be, such that the descent time is a minimum?
Intuition says that it should be a straight line. That would minimize the distance, but the minimum time happens when the ramp curve is the one shown: a cycloid.
Johann Bernoulli posed the problem to the mathematicians of Europe in 1696, and ultimately, several found the solution. However, a new branch of mathematics, calculus of variations, had to be invented to deal with such problems. Today, calculus of variations is vital in quantum mechanics and other fields.
I made the drawing figure of 1/x with desmos graphing calculator. :D
Launch of Apollo 11
On July 16, 1969, the huge, 363-feet tall Saturn V rocket launches on the Apollo 11 mission from Pad A, Launch Complex 39, Kennedy Space Center, at 9:32 a.m. EDT. Onboard the Apollo 11 spacecraft are astronauts Neil A. Armstrong, commander; Michael Collins, command module pilot; and Edwin E. Aldrin Jr., lunar module pilot. Apollo 11 was the United States’ first lunar landing mission. While astronauts Armstrong and Aldrin descended in the Lunar Module “Eagle” to explore the Sea of Tranquility region of the moon, astronaut Collins remained with the Command and Service Modules “Columbia” in lunar orbit.
Sugary Drinks May Slow Down Sperm
Men might want to think twice before grabbing another soda out of the fridge.
Scientists have already shown sugary drinks can add unwanted inches to waistlines, but a new study shows sugar-sweetened drinks such as soda may also lower semen quality.
The researchers found that high consumption of sugary drinks was associated with low sperm motility, or sperm movement — but surprisingly, this was true only for healthy, lean men. The researchers found no relationship between sugary drink consumption and sperm motility in overweight or obese men.
In the study, which was detailed this month in the journal Human Reproduction, researchers analyzed the semen of 189 men between the ages of 18 and 22 from Rochester, New York. Each participant got a physical exam, answered a questionnaire about his health habits and diet, and provided a semen sample.
The researchers relied on the men to self-report how often they consumed sugar-sweetened drinks over the past year, from zero to six drinks per day. Sugary drinks included more than just sodas, said study author Jorge Chavarro, professor of nutrition and epidemiology at Harvard. For example, sports drinks alone accounted for about 40 percent of the sugar-sweetened beverages the men reported drinking.
The top 25 percent of study participants who drank the most sugary drinks consumed an average of 2.7 sugar-sweetened beverages per day. Consuming this many sugary drinks didn’t seem to affect sperm concentration, shape or ejaculation volume, the study found. But the lean men in this high-intake category had 6.3 percent lower sperm motility than their counterparts who consumed, on average, less than one sugary drink per day. One serving was defined as one glass, bottle or can, or roughly 12 oz.
Studies have shown that excess body weight can negatively affect sperm production. Extra fat around the waist and testicles can cause an increase in scrotal temperature, resulting in lower sperm quality. The researchers expected weight to influence the results, because high sugar intake is often associated with a high body mass index, or BMI. However, the results showed an association between sugary drink intake and sperm motility only in lean men. Sperm motility in overweight or obese men was not affected.
Higher sugary drink intake was also associated with lower levels of a reproductive hormone called the follicle stimulating hormone, or FSH. This hormone helps control sperm production, and the men in the study, both lean and obese, who consumed the most sugary drinks had slightly lower FSH levels.
In a recent experiment published in the journal Nature Communications, male mice that consumed one-quarter of their total energy from sugary water had 25 percent fewer offspring than did males on a regular diet. But scientists said more research is needed to determine how sugary drink consumption might influence fertility in humans.
“Fertility could be another reason to look at how many sodas you’re drinking, but there are many other health reasons to watch your intake of sugar-sweetened drinks,” Chavarro told Live Science.