Women's Basketball - February 12-16, 1996
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While I was driving home listening to the pro basketball All-Star game, I was thinking about how, while I like watching women's basketball, men's basketball is often more exciting. Why is that? It's faster, quicker, and higher - there's a lot more dunking in men's ball.When I was a freshman in college it was decided that women should play with a smaller ball, and that this would make the game more exciting since the women would be able to control the ball better. But let's look at what would make the women's game just like the men's (not that this is necessarily a good idea, but let's pretend it is).
Let's say that the average men's college basketball player is 6'3", and the average woman is 5'6". The court is about 78 feet long. The basket is 10 feet high. The free-throw line is 15 feet from the basket. The 3-point line is 19 feet from the basket. The hoop itself is 18" in diameter. How would we need to scale the court down to make the women's game like the men's?
Food for thought: Why won't any of these changes ever be instituted? (This has nothing to do with geometry, but see if you can come up with a reason.)
Annie says: Solutions
Not too many comments this week, but a lot of right answers. A few people got caught in the units of the hoops - it's the only thing measured in inches, and you need to reread your solution and make sure you didn't say something silly like "The hoop is 15.84 feet in diameter," which would make the game considerably less challenging.
Also, don't get carried away rounding things off. I know they probably wouldn't build a court that was 68.64 feet long, but let the builders worry about how to deal with it. We're just going for the straight comparison.
Now for a brief political statement. Feminists needn't rise to the bait here, asking "What's wrong with the women's game?" I never said anything was wrong with it, or scaling would improve it. I said it would make it "just like the men's game," and I added that this wouldn't necessarily be a good idea. I can't imagine ever playing with a hoop that is 8.8 feet high, but that's how it seems to the guys! It's really a whole different game. Having had a long and mildly illustrious basketball career, I'm quite happy the way things are.
And yes, I agree with many of you that it would never happen anyway, because the cost of having two setups would be too great. A lot of places complained when the size of the women's ball was changed and they had to spring for new ones!
Six new schools, this week, including our first from Rhode Island. Following are highlights. The names of all the people who submitted correct solutions and most of the solutions are also available.
Elissa Serrao Grade 9 Mount Saint Joseph Academy, Flourtown, PA To achieve the proper scale of the men's court to the women's, I made a proportion. I put the height of men over the height of women. It was 25/ 22 : the women's distance/x. (I reduced 25/22 from 75/66). From this I concluded the following scale measurements: The Hoop: 25/22 = 18/x The women's diameter is 15. 84 inches The 3 Point line: 25/22 = 19/x The women's 3 point line is 16.72 feet The Free Throw: 25/22 = 15/x The women's free throw is 13.2 feet The Basket: 25/22 =120/x The women's basket is 8.8 feet tall The Court: 25/22= 78/x The length of the court would be 68.64 feet There are many reasons why these changes will never be instituted. First of all, the cost of building all these special new courts would be too expensive. Also, it would make the game to easy for women to play. (I mean, the basket would only be 8 feet tall!)
Jason Lee Grade: 8 School: I.S. 119 Queens, NY Answer: 6' 3" = 75" 5' 6" = 66" 75 : 67 is the ratio of average man to average woman basketball player. For court size: For height of hoop: 75 : 66 = 78 : x 75 : 66 = 10 : x 75x = 66(78) 75x = 66(10) 25x = 22(78) 15x = 66(2) 25x = 1716 5x = 22(2) x = 68.64' 5x = 44 x = 8.8' For free throw line: For 3-pointer: 75 : 66 = 15 : x 75 : 67 = 19 : x 75x = 66(15) 75x = 66(19) 5x = 66(1) 25x = 22(19) 5x = 66 25x = 418 x = 13.2' x = 16.72' For hoop: 75 : 67 = 18 : x 75x = 66(18) 25x = 66(6) 25x = 396 x = 15.84"
Michele Weiss Grade 9 Mount Saint Joseph Academy, Flourtown, PA To make a women's basketball game as exciting as a men's basketball game, you would have to scale down the court and all of the court's components. First I changed everything into inches so it would be easier to work with. I set up this proportion: men's avg. height = women's avg. height size of court X component Then I just plugged in my numbers. Here is what I got: Court component Men's size Women's size 1. length of court 78 ft. or 936 in 69 ft. or 824 in. 2. 3 point line 19 ft. or 228 in. 17 ft. or 201 in. 3. free throw line 15 ft. or 180 in 13 ft. or 158 in. 4. basket diameter 18 in. 16 in. 5. height of basket 10 ft. or 120 in. 9 ft. or 106 in. These changes will never be instituted because of money. They would have to build all new arenas and courts for women. They do not want to spend the money to make the women's game more exciting. It's a man's world!
Melanie Lukens-Bober Grade 9 School: Lincoln Sudbury Regional High School, Sudbury, Massachusetts. Using proportions and ratios, I set up that 6'3"/5'6" (or 75/66) should equal 78/X and then 10/x and then 15/x and then 19/x and then 18/x. I found the following information. The court should be *68.64 feet long. The basket should be* 8.8 feet high. The free-throw line should be *13.2 feet from the basket. The three-point line should be *16.72 feet from the basket. The rim should be * 15.84 inches in diameter. I think that the reason that none of these changes will ever be made is because they are unnecessary. No one would be really happy about them. It would cost a lot of money and take up a lot more space to make individual courts for men and women. It would also offend some women who are trying desperately to be equal to men. It would cause more problems with men and women attempting to play together on teams. Basically no one would ever get around to enforcing it, and these changes would never be instituted.
Dorothy Moorefield Grade: 11 School: Walter Williams High To scale down the basketball court, simply set up proportions using the average height of male basketball players and the average height of female basketball players. Because the proportions would be easier to solve if everything were in the same unit, it is a good idea to convert all the measurements to inches. X = the distance the court scaled for girls 66\x = 75/936 Solve proportions by cross multiplying 75x = 61776 x = 823.68" s = the height of the hoop scaled for girls 66\s = 75\120 75s = 7920 s = 105.6" t = the distance from the hoop to the free throw line scaled for girls t\66 = 180\75 It doesn't matter what order the proportion is set up as long as consistency is maintained. 75t = 11660 t = 158.4" u = the distance from the hoop to the 3 point line scaled for girls 66\75 = u\228 75u = 15048 u = 200.64" k = the diameter of the hoop scaled for girls.(it has to be reduced - we don't want the game to be too easy) 75\66 = 18\k 75k = 1188 k = 15.84" The majority of basketball courts are shared by men and women. It would be too expensive to build a separate court for all the female teams in the world. Also, the changes to the court are only a few inches. These inches are made up for by reducing the size of the ball. Not only is the ball easier to control, it is lighter and requires less energy to move around the court. So if the court were to be reduced, the players would have an easy game. The only thing that might be worthwhile to change would be to lower the height of the hoop to enable more dunking. However, I feel the courts should be left alone because most female players enjoy the extra challenges to their abilities. A female scoring a slam dunk is more impressive to most people than a male scoring dozens of slam dunks.
Heather Booker Grade: 10 School: Smoky Hill High School When solving the problem of the week, I used proportions. I made a ratio with the height of the average man and woman. 5.5:6.25 I then set up proportions with the lengths you gave, making "X" the length or height things should be for a woman. The answers that I came up with are as follows: -Length of the court = 68.64 feet -Diameter of the rim = 15.84 inches -Distance of the 3-point line = 16.72 feet -Distance of the free throw line = 13.2 feet -Height of the basket = 8.8 feet I think they don't make these changes because women are just as capable of playing a sport at the same level of difficulty as a man. Our hands are smaller so the size of the ball does matter a little.
Melissa Sloane Grade 9 Martin County High School, Stuart, Florida First of all we need to convert the men's height 6'3'' to 6.25' and the women's height 5'6'' to 5.5'. Then I took 5.5 over 6.25 equals .88 factor.( 5.5/6.25=.88 factor) Then I drew the basketball court as follows: ------------------------------------------- | ( 10'=8.8') | | rim 18''=15.84'' | | | |---------------15'=13.2'(feet)------------| | | | -------------19'=16.72'(feet)------------| | | | | | | | | | | | | | | 78' | | | | | | |------------------------------------------| men's = women's (10') = 8.8' (18'') = 15.84'' 15' = 13.2' 19' = 16.72' 78' = 68.64' To change the court to fit a woman you would have to make the basket 8.8 feet high. The rim or hoop would have to be 15.84 inches in diameter. The free-throw line would have to be 13.2 feet from the basket and the 3-point line would have to be 16.72 feet from the basket. Lastly the court size would have to be 68.64 feet long. Most women want to play on an equal level as men. They don't want to be catered to. They want to be able to say I play on a man's court and I play well. Also the changes will not be instituted because not many people would be willing to pay for all new stadiums where only women would play - it would cost too much money.
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