Advance mathematics

Name	Discussion
Gpollo 13 years old, New York	Is that advance mathematics like this formula? E = mc2 ?
Arno van Asseldonk, 42 years old, the Netherlands	Mathematics can be studied at several levels. You might consider arithmetic a form of elementary mathematics. It is a matter of convenience which areas in mathematics might be considered elementary, and which areas might be considered advanced. If you wish you might call the mathematics that is taught in primary and secondary school elementary, whereas you might call the mathematics that is taught at the university advanced. The formula that you mentioned stems from a more complicated formula, in which the energy of a given mass m with a velocity v depends on the value of v. If the velocity v is zero, which means that we have a non moving mass, the formula reduces to the formula that you mentioned.
Pattrick-Thailand	I have one probability question. Hopefully someone can help me solve this problem. The story goes like this. There is a committee selection process. The committee body consists of 40 people. The town will put everybody’s name (3,000 unrepeated names) into the box. Then, at each time, they will randomly pick 5 names out of the box. Then, they toss two coins. If the first toss turns out head-tail OR tail-head (ie the two coins turn different sides), they continue with the second toss. If the second toss turns out head-tail OR tail-head (ie they turn different sides again), they continue with the third toss. If the third toss tuns out head-head (it is not ok to turn tail-tail), then these 5 names will be elected as part of the committee’s body. If any of these three tosses do not turn out as determined above at any stage (such as it turns out head-head OR tail-tail since the first toss), these 5 names will be canceled and set aside. Another 5 names will be picked from the box, and then they restart with the first toss again. The process then continues until the body of 40 members is selected as the committee body. In other words, there will be 8 sets of 5 names that meet the three-time toss criteria as explained above. Then, the selection process stops and these 40 people are the committee’s member for that year. In case that they cannot finish finding all 40 people of the committee’s body with the above process and the names in the box run out, then the names that are put aside earlier (ie the names that do not meet the three-time tossing criteria) will all be thrown back to the box and the 5-names picking and tossing process continue again until all 40 members are selected. The questions go as followed. 1. What is the probability that one person in the town get selected as the committee’s member? 2. Suppose each toss takes 10 seconds, (ie. if the three tosses turn out head-tail, head-tail and head-head, it takes a total of 30 seconds. If it tuns out head-head since the first toss, it takes 10 seconds and the first toss restarts again). What is our best guess on the length of time needed to complete the selection of 40- member committee’s body? 3. What is the probability that the process take twice as long as the answer you have in question 2 above? 4. What is the probability that the process take only half as long as the answer you have in question 2 above? 5. How about if these are not fair coins! Suppose the probability of head is only 1/3 and tail is 2/3. What are the answers in question 1 to 4 above? 6. Suppose we change from picking 5 names at a time to 10 names at a time, how long would it take to finish the selection process? I hope that these are fun and someone can help me solve these problems. Please also show how you come up with those solutions. Thank you in advance for your help. Best wish, Pattrick
Pattrick-Thailand	Oh! you can also send me the answer to prakitpom@gmail.com OR share with other readers on this email. Hopefully, we have fun with it.
kmp	I am reading in class v and I want to learn more math
John - Canada	I am trying to draw perspective lines in computer script. For instance I can draw parallel lines by dividing the sides by the number of lines I want to draw. But what I need is a formula to draw horizontal perspective lines. In other words the lines get closer together as you go toward the background. There are many websites that show how to do this using geometry, but I can't find any formula. Thanks.

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