Tennis Results Indian Wells

Written by: on 14th March 2014
BNP Paribas Open
Tennis Results Indian Wells

epa04124306 Sloane Stephens from USA in action against Flavia Pennetta from Italy at the BNP Paribas Open tennis in Indian Wells, California, USA, 13 March 2014. EPA/MICHAEL NELSON  |

* Li beats Cibulkova in Australian Open rematch

* Pennetta back in Top Fifteen after win over Stephens

* Cara Black returns to doubles Top Ten

 

 

Indian Wells

 

Singles – Quarterfinal: (1) Li Na def. (12) Dominika Cibulkova 6-3 4-6 6-3

This was, of course, a rerun of the Australian Open final, and the result was the same. It was a lot closer, though — it took more than two and a half hours, and more than a hundred combined errors, and Dominika Cibulkova had chances to win it. But Li Na managed to hang on — which means that Cibulkova will remain stuck at #11, and still needing a significant number of points to reach the Top Ten. Li is still #2 behind Serena Williams, and a distant #2, but at least she’s increasing her lead over the rest of the world.

Singles – Quarterfinal: (20) Flavia Pennetta def. (17) Sloane Stephens 6-4 5-7 6-4

This should have been over in straight sets. Flavia Pennetta — who to that point had been broken only twice — talked to her coach and served for the match at 5-4 in the second set, and was broken. Two games later, Pennetta was broken again, and a match that appeared to be settled went to a third set. Sloane Stephens — who until the middle of the second set had seemed to be not quite all there — stayed strong at the beginning of the third set, going up 3-0. Only to have Pennetta get the break back as the match passed the two hour mark. Stephens won only one more game as the winds started to really interfere with play.

For Pennetta, this appears to spell a return to the Top Fifteen. If she can somehow make the final, she’ll be #14; lose the semifinal, and she’ll be #15. Stephens, who would have been Top Fifteen had she won this, will have to settle for #16.

Doubles – Semifinal: (5) Black/Mirza def. (8) Hradecka/Zheng 6-4 3-6 10-7

Lucie Hradecka came here ranked #12, but #11 in safe points; Cara Black was ranked #13, and #12 in safe points. That made this, in effect, a battle for a Top Ten spot. And Black gets it; it appears Hradecka will stay at #12. We currently show the Top Ten as follow 1 (1) PENG 8495*

2 (2) HSIEH 8375*

3 (6) ERRANI 7270

3 (6) VINCI 7270

5 (5) SREBOTNIK 7040

6 (3) VESNINA 6835

7 (4) MAKAROVA 6735

8 (11) MIRZA 5705*

9 (9) PESCHKE 5365

10 (13) BLACK 5250*

Rankings

Estimated WTA Rankings As of March 13, 2014

Rank &

Prior

Rank Name Points

1 (1) SWilliams 12660

2 (2) LI 7185*

3 (3) ARADWANSKA 5955*

4 (4) AZARENKA 5441

5 (7) HALEP 4775*

6 (8) JANKOVIC 4590

7 (5) SHARAPOVA 4271

8 (9) KVITOVA 4235

9 (6) KERBER 4050

10 (10) ERRANI 3830

11 (11) CIBULKOVA 3470

12 (13) IVANOVIC 3140

13 (14) VINCI 2925

14 (15) LISICKI 2660

15 (21) PENNETTA 2645*

16 (18) STEPHENS 2625

17 (16) SUAREZ NAVARRO 2620

18 (12) WOZNIACKI 2605

19 (19) BOUCHARD 2485

20 (17) STOSUR 2420

21 (22) PAVLYUCHENKOVA 2240

22 (23) CORNET 2230

23 (20) FLIPKENS 2215

24 (24) MAKAROVA 2125

25 (26) KANEPI 2045

26 (27) CIRSTEA 1910

27 (28) SAFAROVA 1880

28 (29) ZAKOPALOVA 1615

29 (25) Kirilenko 1596

30 (30) KUZNETSOVA 1583

SCORES

 

THURSDAY

 

Indian Wells

Singles – Quarterfinal

(1) Li Na def. (12) Dominika Cibulkova 6-3 4-6 6-3

(20) Flavia Pennetta def. (17) Sloane Stephens 6-4 5-7 6-4

Doubles – Semifinal

(5) Black/Mirza def. (8) Hradecka/Zheng 6-4 3-6 10-7

 

 

Men’s Update *

* Still no Top Ten ranking for Raonic

* Federer cruises again

* Bryans survive all-American contest

 

Indian Wells

 

Singles – Quarterfinal: (7) R Federer def. (17) K Anderson 7-5 6-1

If anything, Roger Federer is just getting better with each match here. This was close to perfect. And it brings a substantial reward: We show Federer back up to #5 in the rankings — meaning that Switzerland joins Spain as one of two countries with two players in the Top Five. Kevin Anderson will probably stay at #18, although there is a chance he could fall to #19.

Singles – Quarterfinal: (28) A Dolgopolov def. (10) M Raonic 6-3 6-4

This was the match that would have put Milos Raonic in the Top Ten — and it wasn’t even very competitive. Raonic had only four aces, and was broken three times (while breaking once); it was over in an hour and twenty minutes. It’s almost as if he’s allergic to the Top Ten.

Alexandr Dolgopolov perhaps didn’t fall low enough to be a real candidate for a Comeback Player of the Year award, but if he’s considered eligible, he’s making a strong case. He’s cut his ranking in half in the course of the last month. He came here at #31; we show him rising to #23. And with plenty of room to go higher.

Doubles – Semifinal: (1) Bryan/Bryan def. Isner/Querrey 6-7(4-7) 6-1 10-7

After a slow start to the year, the Bryans really do seem to be back in form. Let’s hope Sam Querrey can take good things away from this, too.

****** TODAY’S FEATURE ******

 

Ratio of the Circumference….

 

Unless you specialize in a field with a fairly strong mathematical basis, it is very likely that you have never heard of what has been called the most important, or at least the most interesting, equation in mathematics. This is particularly true since there are various forms of it. But we’ll give the most general form:

iπ

e +1=0

That is, if you take the number known as e and raise it to the power of π times i, and add one, you get zero. This is often written

iπ

e =-1

But this form is less useful, because it doesn’t have a zero in it. The first form shows the equation with all its significant parts. The first form is also the one usually cited, under the name “Euler’s Equation,” after Leonhard Euler (1707-1783), who eventually went blind but even so is considered the most prolific mathematician of all time (there is a project underway to republish all his works, and it is estimated that, when finished, a complete set will weigh more than three hundred pounds!). Euler is also regarded as one of the three or four greatest mathematicians; the constant e in the equation is named after him.

Why is this a significant equation? Because it involves so many important numbers. Every one of those five numbers — e, i, π, 0, and 1 — has unique properties and is essential to some branch of mathematics. e is probably the most important number in the calculus; the function ex is famous because it is the only function which is its own derivative and integral. Its inverse, ln(x), is also a “calculus cousin” of the reciprocal function 1/x. The value of e is roughly 2.718281828459.

0 you of course know and love (unless it’s what you have for a bank balance). But it is perhaps more significant than you realize. 0 is the “additive identity” — that is, for any x, x+0=x. To put it another way, 0 is the number such that, if you add it to any number x, the sum is equal to x. There is no other number for which that statement is true. This is important in both arithmetic and algebra.

1 is the “multiplicative identity.” That is, for any x, 1*x=x. Or, 1 is the number by which you can multiply any x and get x again. As with the additive identity 0, this is vital to arithmetic and algebra. 0 and 1 (that is, the additive and multiplicative identities) are so important that, in some systems of mathematics, they are postulated rather than simply counted. Indeed, it is often a key part of an abstract algebra class to prove that, in a particular system, the additive and multiplicative identities exist and are equal to 0 and 1.

i is the square root of minus one. That makes it part of the definition of what are called the imaginary numbers, and of the complex numbers. The significance of this is rather hard to describe if you haven’t had any exposure to complex numbers, but a complex number consists of a real number (such as 5, or √3, or 4/9) and an imaginary number (3i, or √37i). The complex numbers — which are defined in terms of i — are extraordinarily important in signal processing and in dealing with electrical and magnetic fields (which means that they probably figure into ShotSpot and its relatives, somewhere in some deep and mysterious way), and they are also vital to many mathematical disciplines. The so-called “Fundamental Theorem of Algebra” — which is truly a vital result — is that every algebraic equation with complex coefficients has a solution among the complex numbers. This is, we know, getting way, way off-topic, so we’ll leave it there. But trust us — i is a very big deal.

And then there is π. Unlike e and i, you have almost certainly dealt with it at some time in your life. It’s the ratio of a circle’s diameter to its circumference. It’s the ratio of a circle’s area to the square of its radius. It is used to compute the surface area and volume of a sphere. If by some chance you have a four-dimensional hypersphere somewhere around your house, you can also use π to measure some of its dimensions. That’s right — π even measures the dimensions of shapes that don’t actually exist in our observable universe. Its value is roughly 3.141592654.

And, because π is so famous, it actually has its own day — “pi day.” Which, for obvious reasons, is March 14 (3.14, get it?). Mathematicians sometimes celebrate by having a piece of pie. They also urge people to go out and look for items related to π.

So, in honor of pi day, we’re going to have a look around the tennis court.

The first thing is obvious: The tennis ball. It’s round. That means that you need to know π to determine its circumference, its surface area (a big deal in determining air resistance!), and its volume. Also such things as its inertia. And, since tennis balls spin in flight, you need to use π to calculate their stability and the curvature of their flight.

And when you swing at the ball, your arm pivots around a particular point (your shoulder). That means that the course of the racquet follows along an arc of a circle (modified, to be sure, by the movement of the elbow and wrist. But those too pivot around a particular point. Thus the motion of the racquet is the sum of three circular paths).

There is also a relationship between π and the ball’s rise and fall under gravity, but it runs through calculus and that eiπ+1=0 relationship above; we won’t go into that except to mention it.

But it is worth mentioning that the head of a tennis racquet is an ellipse — a shape which, just like a circle, is measured in terms of π. Think that doesn’t matter? The people who are designing the racquet to get the largest possible “sweet spot” would disagree….

There is another important point about racquet design, and that’s stress on the strings. A badly-formed racquet head will stress the strings very unevenly, meaning that the strings are more likely to break at some places than others. It doesn’t really matter to the user where the strings break, of course — but if there is a spot subject to breakage, that means that strings will break more often, and that obviously does matter to the user. So racquet designers need to construct careful mathematical models, involving π, of the shapes of their racquets.

That’s about it for uses of π in the equipment, since the court is rectangular (although the author can’t help but wonder what it would be like to play on a circular or elliptical court). But the downward curve of the net between the posts and the center is calculated using the hyperbolic trigonometric functions, which involve e and π although not i. For that matter, net posts are circular. The strings of the net are set in a square array, but you need to use π to figure out if a ball can possibly go through the gaps in the net. The camera lenses which record the match are circular. So are the eyes with which you watch it. When players fly from tournament to tournament, they fly along a great circle arc — and the length of that great circle determines the flight distance, and hence their frequent flyer miles. And you need π to measure that. So π affects players even when they’re between tournaments. Having too much pie may not be good for your tennis game — but without π, you wouldn’t be playing….

 

RANKINGS

 

Estimated ATP World Tour Rankings

As of March 13, 2013

Rank &

Prior…Player………..Points

1..(1) Nadal………….13130

2..(2) Djokovic……….10080

3..(3) Wawrinka………..5650

4..(4) Ferrer………….5150

5..(8) Federer…………4805

6..(6) Murray………….4795

7..(5) Berdych…………4540

8..(7) Del Potro……….4270

9..(9) Gasquet…………2905

10.(10) Tsonga………….2615

11.(11) Raonic………….2575

12.(13) Isner…………..2490

13.(12) Haas……………2435

14.(14) Fognini…………2295

15.(15) Youzhny…………2135

16.(16) Dimitrov………..2130

17.(17) Robredo…………2040

18.(18) Anderson………..1940

19.(19) Almagro…………1795

20.(20) Janowicz………..1715

20.(21) Nishikori……….1715

22.(22) Gulbis………….1706

23.(31) Dolgopolov………1555

24.(25) Monfils…………1520

25.(24) Kohlschreiber……1510

26.(26) Cilic…………..1500

27.(23) Simon…………..1485

28.(27) Pospisil………..1343

29.(33) Verdasco………..1270

30.(30) Tursunov………..1247

 

 

SCORES

 

THURSDAY

 

Indian Wells

Singles – Quarterfinal

(7) R Federer def. (17) K Anderson 7-5 6-1

(28) A Dolgopolov def. (10) M Raonic 6-3 6-4

Doubles – Semifinal

(1) Bryan/Bryan def. Isner/Querrey 6-7(4-7) 6-1 10-7

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