Pythagorean Theorem

In my last trip from Queretaro to Juarez (yeah, a lot happenned during that trip, jeje), we left my mom in Chihuahua (she had some family stuff to take care off) so it was only my dad and me in that last four-hour drive to Juarez. Both of us are real math hobbyist, and for some reason we ended up talking about the pythagorean theorem and the fact that neither of us, even though we use it for everything now, haven't seen it's proof in any text book we've read. It's such a used theorem, that it's difficult to think a proof for it. I remembered one, using the areas of the squares formed by the each of the sides of the right triangle, but that it's just a case-by-case proof, I'm more into generalized theorems.

Anyway, I had a small notebook with me so, with three hours of boredom ahead, I decided to prove it. An hour and a half later (which frankly felt more as half an hour), this is what I came up with:

The equation on the bottom starts with an equality of areas: the area of the big square is the square of c, which also is equal to the sum of the area of the four right triangles and the area of the small square; it's just simple algebra from there on.

After I got home, I did a little research and imagine my surprise when I read that this theorem has around 370 proofs, all using from trigonometry, calculus, to finite math. Apparently my proof was actually done around two and half millenium ago, documented in the chinese text Chou Pei Suan Ching done between the year 500 to 200 BC, which right now is the first official documentation of a proof for such theorems; there have been others before, but none of them were documented for that purpose (it was more of a collateral thing in those). Actually, this proof is so famous in China that the Pythagorean Theorem is better known as "Gougu Theorem", based on the numerical proof in the Chou Pei Suan Ching, presented in The Arithmetical Classic of the Gnomon and the Circular Paths of Heaven.

In all fairness, the mayority of those proofs used trigonometry and calculus which, in themselves, use the pythagorean theorem for their own internal proofs (which sounds incongruent). The Chou Pei Suan Ching proof (mine) uses algebra and analytical geometry which doesn't rely on Pythagoras to be proven. So... yeah, I rock, jeje.

[This post was heavily based on the wikipedia article of The Pythagorean Theorem.]

EDIT: After further research I found that the Chou Pei Suan Ching proof was just for the case of the (3,4,5) triangle; it wasn't a general proof like mine. The first person to have actually proven it like I did was the Indian mathematician-astronomer Bhaskara Achārya; you can see evidence of this if you look him up, or in the first Addendum of this page.

The Road from Hell...

In my latest (and probably last) trip from Queretaro to Cd. Juarez, I ran into what I'm now calling the "Almost Road from Hell". 'Almost' because that "Road from Hell", at least for me, belongs to 10 km between Durango and Mazatlan here in Mexico known as the "Espinazo del Diablo" (literally, the Devil's Backbone) and you need a good stomach to withstand it because, well, take a look for your self:

Courtesy of MapQuest

That's an estimate of the land. Look at those curves!

Anyway, the "Almost Road from Hell" is a temporary one (I hope). It's a 65 km long patch of a road starting in the limits of San Luis Potosi city going towards Zacatecas (the blue part):

Courtesy of MapQuest

Compared to the Devi'ls Backbone, it may seem less daunting (which, in retrospect, it is), but don't let that deceive you. This "patch" is being repaired, by little chunks at a time. You're welcomed by repaired chunk 2 to 3 kilometers long followed by an unrepaired chunk 10 to 15 kilometers long, then a repaired one, etc. If you're driving in the repaired chunks, you'll be joyfully driving by speed bumps every other 250 m. That's right, speed bumps in a road equivalent to an U.S. interstate highway, with three lanes going each way (Did I say that they were very wide as well as tall bumps? No? Well, they were). If you're driving in the unrepaired chunks, you'll get one lane going each direction (So, talk about a complete deadlock when entering each one of these!) and speed bumps (yes, also) every other 500 m. Because there are a lot of semis and big trucks transporting stuff very slowly, these three factors (one lane, speed bumps, and slow semis) make it near to impossible to pass them, thus, you're forced to go around 20 km/h (~13 mph) for the length of the unrepaired chunk.

After we cleared it, my dad and I did a little math, and this is what we came up with:

  1. The patch is around 65 km long.
  2. We spend a little over 1 hour and half to clear it (pure hell, I tell you!).
  3. -> 65 km/1.5 h = 43.33 km/h ~ 27mph

This is close to the high speed limit of some residential areas in Mexico!

So, from right now until (I hope) the end of this year: AVOID GOING THROUGH THE SLP-ZACATECAS HIGHWAY, if we could call it that.

GDGraph in "Map my Run"

Well, I'm happy to report that GDGraph is being used quite happily by the Webmaster of Map my Run, which for me is completely encouraging to continue moving on with this project. He's given us credit in the last question of this FAQ.

Who knows? Maybe it'll move on to second place above Libchart in Hotscripts where we stand on third place in the freeware graph PHP classes. First place is quite a long shot: JpGraph is very hard to beat right now, but I'll settle with second for now =).

EDIT: (2010-09-01) I don't know when this happened, but "Map my Run" isn't using GDGraph for PHP anymore. Pity.

Caleb's Definition

—Biblical Data:
According to the Biblical text, Caleb was of the tribe of Judah. He represented that tribe among the twelve spies whom Mosessent from the wilderness to spy out Canaan. He and Joshua alone brought back an encouraging report, and in consequence were the only ones of all that came out of Egypt who were permitted to survive and enter Canaan (Num. xiii. 6, 30; xiv. passim; xxvi. 65; xxxii. 12; xxxiv. 19; Deut. i. 36). After the conquest he was given Hebron and the region around it. In the conquest of this territory he offered the hand of Achsah, his daughter, to the man who would capture Hebron for him; the feat was accomplished and the maiden won by Caleb's younger brother, Othniel. To him was assigned the south land, to which later, at Achsah's request, "the upper springs" were added (Josh. xiv., xv.; and Judges i. passim). His name is connected with several towns in southern Judah (I Chron. ii. passim).J. Jr. G. A. B.

—In Rabbinical Literature:
In the rabbinical sources, Caleb, the son of Hezron (I Chron. ii. 18-20), is identified with Caleb, the son of Jephunneh (Num. xiii. 6), the epithet "Jephunneh" having been given to him because he "turned away" from the sinful intention of the other spies who advised the people against going into the Holy Land. Caleb is also called (I Chron. iv. 5) "Ashhur," because his face became black from much fasting, and "father of Tekoa", because he fastened his heart on God, and in this faith he married the prophetess Miriam, whom, although she was neither fair nor healthy, he treated with fatherly love, appreciating her own piety and her relationship to such brothers as Moses and Aaron.
Although the son of Jephunneh, Caleb is also called "the Kenizzite" (A. V., "Kenezite," Josh. xiv. 6, 14; compare Judges i. 13), because Kenaz, the father of Othniel, was his stepfather; Othniel thus being in fact his half-brother (Soṭah 11a, 12a, where the names of Azubah's children [I Chron. ii. 18] are applied to Caleb in haggadic fashion; see also Ex. R. i. 17).
When Caleb came to Palestine as one of the spies, he visited the graves of the Patriarchs in Hebron (compare Num. xiii. 22) and prayed for their help against the sinful intention of his colleagues (Soṭah 34b). It was also he alone who insisted that the spies should take some of the fruits of the country with them in order to convince the people of the extraordinary fertility of Palestine. As they did not wish to do this Caleb drew his sword and said: "If you will not take any fruit with you, then either my life or yours!" (Tan., Shelaḥ 15, ed. Buber; Num. R. xvi. 14). Thoroughly realizing the evil intentions of the spies, and knowing that it was useless to attempt to dissuade them, he did not betray his plans to them, but acted as if he agreed with them (Tan., l.c. 19; Num. R, l.c. 19). But when the spies began to incite the people against Moses, and hissed Joshua, who attempted to act as peacemaker, Caleb, whom they had thought to be on their side, rose and said, "This is not the only thing the son of Amram has done for us."—here all the ring-leaders were silent—"He has taken us out of Egypt; he has divided the sea for us; and he has fed us with manna. Now, therefore, if he were to command us to make ladders and scale the heavens, we should obey him. Let us go up at once and take possession" (Soṭah 35a; Num. R. l.c.; Tan., l.c.). When the country was divided, Caleb and Joshua received the portions that had been intended for the other spies (B. B. 117b, 118b).
Caleb was the father of Hur from his second wife Ephrath (I Chron. ii. 19), and, therefore, the progenitor of the Davidic house, the "Ephrathite" (I Sam. xvii. 12; Soṭah 11b; Sanh. 69b).J. Sr. L. G.

—Critical View:
The eponymous ancestor of the clan of Calebites. Since "Caleb" signifies dog, it has been thought that the dog was the totem of the clan. Modern criticism finds several different strata to this material, representing different points of view. The oldest writer (J) calls him simply Caleb in Josh. xv. 14-19; and Judges i. connects him with the expulsion of the sons of Anak from Hebron, and with the gift of Achsah and of certain lands to Othniel. D and P call him Caleb, the son of Jephunneh, and make him one of the twelve spies. In the original form of the story he alone brought back the favorable report, and so of all that came out of Egypt he alone entered Canaan.

By the way...

Almost forgot:


Left alone...

Much has changed, but apparently I'm willing to let go of so few things...

They're together, I don't know if they're together right now, but they're together... I saw, I know them so well (or, knew them) that they're with each other as they have always been, I was just making myself believe that they weren't.

I don't know what's hurting more: the fact that I have feelings for her (which I have no idea where are they coming from, I know that she's gone, I know I shouldn't be with her, but... here I am), the fact that I STILL have feelings for her after all of this, the fact that it's very probable that I won't fit in with them from now on making it to be the most alone that I've been since before high school... they're the closest thing that I've got (for now, apparently) to real and sincere friendship.

Deep down, I'm really happy for them, I know... but the beginning of the end had appeared since such a long time ago, and I played dumb, to avoid the pain. Right now it's all sinking in, and it hurts, so bad. I miss us, not Julia and me, but Julia, Hugo and me; we went out, and we weren't there, I've tried, I've forced it a few times, but it wasn't there... just, they were there, and me aside. It never hurted so much to be the third wheel: it even hurted more than that time that I was the 12th wheel (yeah, four couples, and one threesome; beat that!). Little by little I saw my two best friends happy with each other (which, yes, made me happy), and my presence forcing them to include me... maybe I'm making too much of one outing, but right now I'm up to the point that I don't want to hope anymore, it hurts to hope... and hope what? That Hugo will always be there? He will, I know he will... for Julia to think of me as more than a friend? She won't, I know she won't...
But there's this sense of support that always came from them that has begun to fade away; it's weird, it's probably the other way around, I know Julia cares a rat's ass, but Hugo did took a little more interest in my opinion, and for some reason he took my "blessing" very welcoming.

I'm crap right now, I'm nothing right now, which I should be fine with, but I always thought feeling like nothing also came with feeling nothing... guess not... and that's what I want, to feel nothing, to look at them and feel nothing, just as they probably will feel towards me, cuz they sure have showed that that will be our situation in the near future...

Ultimo día en Quéretaro

Siendo éste mi último en Querétaro, decidí escribir en español. Esto de los & para escribir con acentos es más tedioso de lo que recuerdo. O perdí costumbre...

Me siento bien, voy hacia lo que quiero hacer de mi vida. Mañana me dirijo a Juárez para quedarme un mes ahí para visitar a mi familia y mis amigos de por allá, aunque me da algo de miedo... han estado ocurriendo cosas en las que no sé si encajo, es seguro que el tiempo ha pasado y estar tan cercano por tanto tiempo a amigos de allá me lo va a mostrar de una manera muy directa y sin escrúpulos... jeje, en iTunes acaba de comenzar Breathe Me de un grupo llamado Sia que me presentó una muy buena amiga mía de aquí llamada Cristina Bringas (traté de buscar su blog, pero no lo encuentro, perdí mis bookmarks en el reformateo): no sé como tomarlo. A lo mejor nada más como "suck it up and deal with it when it comes". Uno de mis amigos (Hugo Cervantes, se podría decir que es mi mejor amigo de todos los tiempos con buen porcentaje de estar en lo correcto) me ha estado mandando mensajes, de la manera que el sabe que me gustan: mentando madres, pero a la vez con cierto cariño sutil declarando que me quiere. Es agradable sentir que tan siquiera algo no ha cambiado, pero el cambio es inevitable, hasta del que no se quiere que suceda ... ya saben adonde me estoy dirigiendo...

Es extraño: lo platiqué con mi madre hace poco (sí, me llevo muy bien con mi mamá en ese sentido, no soy muy dado a tener muchos confidentes en ese tema), y me ayudó... usualmente platicarlo ayuda. Aun así me siento raro, algo que sé que no debería estar sucediendo, debo seguir con mi vida, pero hay algo que no se deja ir; ojalá que este tiempo cercana a ella me proporcione de algo que permita que esa parte de mi que quiere algo más de esa relación (si la pudieramos llamar así, porque francamente ya se ha reducido a... pues... nada) dejarlo ir, franca y sinceramente... verla y no sentir nada, solo un bonito recuerdo, como ella al parecer se siente hacia mí...

No soy dado a pedir suerte, porque usualmente cuando se desea hay algo de la situación que se puede controlar... me gusta que me deseen éxito, porque implica que hay algo de control de mi parte, de alguna forma le pide al subconciente a estar alerta (y, francamente, me he dado cuenta que desear buena suerte a alguien le trae mala suerte, jeje)......... en este caso, supongo que ese deseo es apto: He decidido no controlar absolutamente nada de mi visita. Si algo tiene que suceder, que suceda; si quiero que suceda algo (como ver a algún amigo, etc.) voy a hacer lo posible que suceda, si no sucede, me va a doler y dejaré que me duela, ya me cansé de estarme protegiendo, que se me mate de una vez, ya tendré mucho tiempo para sanar en Inglaterra, pero no me iré sin un "tal vez" o un "si hubiera" en mi cabeza antes de irme. Prefiero el dolor de ver qué sucede a la agonía de no saberlo.

¡Se cuidan! Y nos vemos en Juárez.

Eating my words...

Apparently the British Embassy in Mexico just sucks when answering the phones, because, when I went and personally delivered my documents for my student visa, the person (which I knew, from her voice, that she was the same person that "assisted" me on the phone) was very kind, chatty, and patient. She even comment me about my name and asked me if I knew it's meaning, which I do (but that's a subject for a whole other post... mmm... maybe the next one, haven't done a big one in a long time); she asked me if I knew it's mayan meaning, which I didn't (I'm writing this around five days after the encounter and haven't found information about it's mayan meaning... weird). She went on that her son has this weird name which is in french, and that it has evolved to just "Roy".

There were two other soon-to-be british students in front of me who were abruptly called back to their seats because of incomplete documentation (one of them came with a printout of an email of acceptance of the Alban Scholarship, which, frankly, would've been a very obvious red flag when reading the outline and instructions in the webpage and printouts taped to the outside and inner office walls... the other one didn't even bother to fill out the application form... no wonder the british lady was so fed up when I called her). When I was called forth after, having being a witness of the all-familiar wrath of this red-tape-experienced old lady, I was ready to pee in my pants, but was pleasantly surprised by her attitude... I would like to credit that to the fact that I did a little subtle but, in my opinion, enjoyable joke in my encounter "well, ma'am, keeping with the M.O. here, I too am here for a student visa" (I never said it was a good one, jeje); but maybe because I prepared myself (thanks largely to my mom and her paperwork), few questions were asked because I've already had the rest answered by phone previously. The lady probably thought "finally, someone with everything complete"; she even offered to do it in 24 hours (not the published 48) seeing that my permanent address was in Chihuahua (19-hour bus-ride), which I kindly denied "I'm living in Queretaro right now" (3-hour bus-ride) "so there's no need to hury things that don't need to be huried"; she grinned.

So, yes: I'm officially eating my own words... A piece of advise (mmm... Matrix... I'm so watching it after finishing up this post): if you're going to apply for a student visa for the U.K. here in Mexico, prepare yourself before hand (read their webpage, it's very complete, it even comes with a map explaining how to get there, which I gave to the cab drivers that picked me up in the airport; both of them told me that the map helped a lot and that very few cab drivers know how to get there), if you have any questions about anything that's not on their website call them and, remember, be very patient (the lady there is very stressed out), when your turn is up try to start out with a joke and end with some kind remark, the lady there will be very pleasant if you show her that you've done your homework... oh, and change your name to something with a mayan meaning, it apparently helps =)

Bored, cold and british...

Installing XCode 2.3 (java documentation indexation takes way too long)...

Doing it out in the open, where (thanks to the Weather widget in my dashboard) its 22 °C, and that with only a T-Shirt on (jeje, well, with pants too... yeah, for some persons that know me that actually needs to be instated) is very very cold... well for me... crybaby, I know.

... British Embassy in Mexico sucks!!! "You have doubts? How come?? We've explained everything in our webpage!!!" Uhmmm...

  • what happens if I don't have some information that's needed in the AV1 form (like a fax number) "Oh, well, just put NA" (not on the webpage)
  • i'm thinking of doing a PhD after the masters, do i put down the length of my studies including the PhD or do i extend my visa stay after finishing the masters? "just put down the length of the masters and extended after" (not on the webpage)
  • it says here that i enlist any properties that are at my name, do i put on my car? is that accepted? "whatever....." (well, that's the only answer that i agree that it shouldn't be on the webpage because of it's rudeness)

yeah, so... yeah... bored... and cold... with a british twist... get the title? huh? HUH?? =) © <- for ishbel, i'm splitting the copyright profits with her