Great Lakes Science Center has a new periodic table of chemical elements exhibit thanks to a donation from the Northeastern Ohio Science and Engineering Fair (NEOSEF). NEOSEF donated the funds for the exhibit in honor of Dr. Glenn Brown and Dr. Jeanette Grasselli Brown.

Great Lakes Science Center board member Tom Brick, Jeanette Grasselli Brown and Science Center President & CEO Dr. Kirsten Ellenbogen.

Michelson–Morley Experiment Conducted in 1887 by physicist Albert A. Michelson of Case School of Applied Science and chemist Edward W. Morley of Western Reserve University.

Michelson-Morley Experiment marker at CWRU

Big Numbers Geek Math

Sometimes we throw around numbers like a million or billion or trillion or more very casually. It's good to have a frame of reference to compare to.

For example, 1,000 seconds is almost 17 minutes. One million seconds are counted off in about eleven and a half days. But it takes 32 years for one billion seconds! That's how much bigger a billion is to a million.

A trillion seconds would amount to no less than 31,709.8 years!

Think of that when you hear of trillion dollar deficits and budgets.

6174 is known as Kaprekar's constant after the Indian mathematician D. R. Kaprekar. This number is notable for the following property:

Take any four-digit number, using at least two different digits. (Leading zeros are allowed.)

Arrange the digits in descending and then in ascending order to get two four-digit numbers, adding leading zeros if necessary.

Subtract the smaller number from the bigger number.

Go back to step 2

The above process, known as Kaprekar's routine, will always reach its fixed point, 6174, in at most 7 iterations. Once 6174 is reached, the process will continue yielding 7641 - 1467 = 6174.

The only four-digit numbers for which Kaprekar's routine does not reach 6174 are repdigits such as 1111, which give the result 0000 after a single iteration. All other four-digit numbers eventually reach 6174 if leading zeros are used to keep the number of digits at 4.

The Great Lakes Geek often gets questions about gambling and the lottery. Just the other day I was asked to figure the odds of a tossed coin landing on 'heads' after 9 'heads' were tossed in a row.

I explained and the person still does not believe the answer. I told him that if a fair coin is tossed and heads comes up 9 times in a row it has no effect on the next toss. A coin has no memory so there is still the usual 50-50 chance of tails or heads. The previous 9 or 900 tosses have nothing to do with that next toss.

The confusion is about the probability of tossing 10 'heads' in a row. That's a whole 'nother smoke.

The probability of one head in a row is 1 out of 2 (.5), the probability of 2 heads in a row is 1 out of 4 (.5 x .5), 3 heads is 1 out of 8 (.5 x .5 x .5) and so on. So the probability of 10 heads in a row is 1 out of 1024 (.5 to the 10th power) or .0009765625.

In a real world case where someone tosses 9 heads in a row I would be concerned about the fairness of the coin.

The last post about the probability of tossing a coin and getting 10 heads in a row prompted a question about the lottery. The conversation between Leonard's mother Beverly and Sheldon on the Big Bang Theory comes to mind:

Beverly: Is that a rhetorical point, or would you like to do the math?

Sheldon Cooper: I'd like to do the math.

Beverly: I'd like that, too.

Here we go. Say there are 44 possible numbers and you have to pick the lucky 6 to win. How many ways are there of choosing a 6-number combo from the 44?

The formula is C (44,6) which is 44 factorial divided by (6 factorial x 38 factorial) or 44! / (6! *38!). Then the probability of coming up with a specific 6 number combination is 1 over that number.

Refresher: Factorial is the product of that number and all the positive integers less than it. So, 6 factorial, designated as 6! is the product of 6x5x4x3x2x1 or 720. Factorial get huge fast. For example, 10! is 3,628,800. So 44! is huge and 1/44! is minute.

To see the chances for a particular lucky number being in the selected 6, you want to find the probability that the winning 6 number combination will contain any given number. First, you want to figure out how to not pick that number.

You have to choose the 6 numbers from the other 43 so use the formula C(43, 6). There are C(44,6) - C(43,6) combinations which include your lucky number.

The probability is then that result divided by C(44,6).

The Cleveland Botanical Garden has a permanent Glasshouse display with an environment of the Spiny Desert of Madagascar. Amid a world-class collection of endangered plants are exotic animals, including chameleons, a yellow-throated plated lizard and three radiated tortoises. Here you'll find one of the largest collections of Madagascan baobab trees under glass in the United States.

In this video a volunteer shows 'Bob' and another chameleon up close.

Here's another very basic math exercise since you asked for more. If you want to quickly multiply a two digit number by 11, here's the shortcut.

Let's use 23 x 11 as the first example. The first number will be the 2 from 23 and the last number will be the 3 from 23. In the middle, put the sum of the number, 2+3=5. So 23x11=253.

Try 42x11. The answer starts with 4 and ends in 2 and the middle is 4+2=6 so the answer is 462.

There's a little hitch when the sum is greater than 10. Try 76x11 for example. The answer starts with 7 and ends in 6 but when you add up the 7+6 you get 13. You don't put 13 in the middle, you put the 3 in the middle and add the 1 to the first number, the 7. So 76x11=836.

If you line up the problem like you learned in school, you will see why it works. You are multiplying by 1 so basically writing down the number twice, but shifted over the second time. Only the middle gets added - the start and last number never change.

Get it?

The Answer is 1089

Geek Math Trick

Here's a very basic math exercise that won't amaze your friends but will get them thinking. The Geek likes to pretend he is opening an envelope a la Johnny Carson's Carnac or writing it on his arm or something.

Pick a three digit number of different numbers (so 123 or 487 are OK but 111 or 232 are not) Let's use 816 as an example.

Reverse the number. So 816 becomes 618

Subtract the smaller number from the larger. 816-618=198

Reverse the answer number. 198 becomes 891

Add that number to the answer of the subtraction. 891 + 198 = 1089

Voila! The result is 1089!

It's simple to prove with a little Algebra - Let the Geek know if you can't figure it out. It's based on the places of the digits so if you choose a number like 546 the process will be 645-546=99 and 99+99=198 not 1089.

You have to look at it like 99 is really 099. So 990-099=891 and 891+198=1089

Note also that it may not work with repeated digits because if it's a palindrome like 575 when you reverse it you will also get 575 and the difference will be 575-575=0 so there is nothing to work with.

Do girls understand the power of STEM to change the world?

In partnership with Global Ties U.S. and the U.S. Department of State, the Cleveland Council on World Affairs (CCWA) welcomed local leaders in civil society, government, and business, along with leaders in international exchange programming throughout the country, to highlight the region's public diplomacy initiatives and specifically how women have played a key role as Citizen Diplomats.

The Women in STEM panel focused on the role and social impact of Women in STEM. The moderator was Dr. Evalyn Gates, former CEO of the Cleveland Museum of Natural History and the panelists were Feowyn MacKinnon, Head of School of MC (squared) STEM High School and Dr. Marla Perez-Davis, Deputy Director, NASA Glenn Research Center. Dr. Gates asked the panelists if girls really understand the power of STEM and how it can change the world.

It's been a long time since the Great Lakes Geek studied topology and he wasn't around when they used this book. But it's great to see John Kelley's classic graduate level textbook from the 1950s-70s in general topology available online in a variety of formats for free.

This video shows how the world's most famous photo actually got captured and how the 3 astronauts had to scramble to get color film in the camera and roll the module. Very cool.

Feynman Lectures on Physics

Geek Link

The famous Feynman Lectures on Physics is a physics textbook based on some lectures by Richard P. Feynman, a Nobel laureate who has sometimes been called "The Great Explainer". The lectures were given to undergraduate students at the California Institute of Technology (Caltech), during 1961-1963 and have been a favorite for aspiring physicists ever since.

The three volumes of the book focus on mechanics, radiation, and heat, including relativistic effects (Vol 1), electromagnetism and matter (Vol 2) and quantum mechanics (Vol 3).

In case you didn't know (or forgot) in 2013, Caltech in cooperation with The Feynman Lectures Website made the book freely available, on the web.

As the site says, "Now, anyone with internet access and a web browser can enjoy reading a high quality up-to-date copy of Feynman's legendary lectures.
This edition has been designed for ease of reading on devices of any size or shape; text, figures and equations can all be zoomed without degradation.

A photobombing squirrel helped a Northland College student document the highest recorded observation of the gray tree frog in northern Wisconsin.

As part of a larger study of old and large white pine canopies, Northland College senior Madison Laughlin of Edmonds, Washington, documented the tree frog almost 70 feet above the ground - more than double the highest previously on record. Her findings were published in the May issue of the scientific journal, Ecology.

"This frog appears to be able to weather sun during the day in the canopy by finding shady and cool spots,"¯said Laughlin, who studies natural resources and geology.

As part of the study, Laughlin and her tree-climbing professors set up three motion sensitive cameras in three white pines to observe life at the tops of the trees. They have already identified 17 species of animals - squirrels, birds, mice, and tree frogs - as well as a mushroom species, a variety of insects and many lichen species particular to this special habitat.

Madison Laughlin

"This is research that is literally being done in our backyard," said Assistant Professor of Natural Resources Erik Olson. "That is one of the beautiful things about science - we don't have to go to the ends of the Earth to make new insights into our world."

In this case, capturing frogs in unexpected places. Tree frogs are small and similar in temperature to their environment so do not set off the motion sensitive cameras. However, flying squirrels do. And on four different occasions, flying squirrels have exposed tree frogs up high.

"It was really exciting to find something that wasn't a squirrel," Laughlin said of looking through hundreds of collected camera captures.

Laughlin says that there is a gap in what we know about tree frogs. "Oddly, there isn't much research on tree frogs in trees. Most of the research is about their breeding, which takes place in ponds," she said. "This research is helping open the door to the vertical dimension of habitat."

These images suggest a higher level of habitat usage in the tops of trees than previously thought. "I love forestry and forest ecology,"¯Laughlin said. "And I've never thought about the three-dimensional aspect of habitat - there's a lot going on up there."

Additional work is underway to describe the habitat usage of other animals high in the trees and to begin to answer the question of why tree frogs go so high.

"We're not surprised that the canopy is an important habitat, but we are surprised how many and what species are up there and how often they visit," said Assistant Professor of Forestry Jonathan Martin who is co-directing the research. "The combination of the scale and growth patterns of these trees as well as the habitat surprises gives me a renewed appreciation for the complex processes occurring high off ground."