Math Fun Facts Did you know that it is possible to cut a solid ball into 5 pieces, and by re-assembling them, using rigid motions only, form TWO solid balls, EACH THE SAME SIZE AND SHAPE as the original? This theorem is known as the Banach-Tarski paradox. So why can't you do this in real life, say, with a block of gold? If matter were infinitely divisible (which it is not) then it might be possible. But the pieces involved are so "jagged" and exotic that they do not have a well-defined notion of volume, or measure, associated to them. In fact, what the Banach-Tarski paradox shows is that no matter how you try to define "volume" so that it corresponds with our usual definition for nice sets, there will always be "bad" sets for which it is impossible to define a "volume"!
25 Beautifully Illustrated Thought-Provoking Questions A question that makes you think is worth asking… At the cusp of a new day, week, month, or year, most of us take a little time to reflect on our lives by looking back over the past and ahead into the future. We ponder the successes, failures and standout events that are slowly scripting our life’s story. This process of self reflection helps us maintain a conscious awareness of where we’ve been and where we intend to go. It is pertinent to the organization and preservation of our dreams, goals and desires.
10 Simple Postures That Boost Performance Psychological research suggests simple actions can project power, persuade others, increase empathy, boost cognitive performance and more… We tend to think of body language as something that expresses our internal states to the outside world. But it also works the other way around: the position of our body also influences our mind. Clear Skin From the Inside Out : Green Smoothies Green Smoothie In, Radiant Glow Out Her 5-year-old butt sat firmly planted on the chair, not by will. By force. Psychic mom-force. Giant, wracking sobs shook her body, as she swallowed for air through the hands over her tortured mouth.
China vs United States As we discussed in yesterday’s post, whether the United States and China like it or not, the economic futures of both countries are intertwined. Everyone knows that China’s got more people and that its importance as an economic superpower has escalated in recent years. What you might not understand is how the differences between our countries, in economic philosophy, in population, in geography and in how the military is built and paid for ultimately play into the entire economic relationship. Amazing Coincidences Weird Stuff Life is full of coincidences, some very minor, but occasionally – extraordinary. This is a list of 15 of the most incredible, unbelievable coincidences. 15. Family tree of the Greek gods Greek cosmological entities Essential Olympians and Titans The essential Olympians' names are given in bold font. See also
10 Basic Truths About Keeping Your Relationship Healthy I think it's easy to make things more complicated than they need to be. Here are some basic rules of the relationship road that will keep you headed in the right direction. 1. Successful relationships take work. They don't happen in a vacuum. They occur when the couples in them take the risk of sharing what it is that's going on in their hearts and heads. 101 Revolutionary Ways to Be Healthy Do the healthy thing, even when it's challenging, inconvenient or considered weird. Take pride in that. Just because it's popular doesn't mean it's smart or good for you. Enlist fellow trend buckers and create a trend of your own. Use your healthy frustration about the unhealthy status quo to spark creativity and determination. Look for signs of progress (beyond pounds lost) and rejoice when you find them.
Is College Really Worth It? Is going to college really worth it? Probably so, but it's not that clear cut, and economics have been arguing the point for 30 years. Most studies tend to show that college-educated people end up making far more money in the course of their lifetimes. (The niggle: Usually, it's not worth paying for a private university.) Still, that evidence isn't totally cut and dry: What do you really learn in college? Is what you learned in college really what's producing the value? Health Fun Facts Absolutely True! The safest number of times to reuse a disposable razor is only 3. Disposable razors have thinner blades than other razors, and are thus more prone to producing microscopic cuts in the skin.