La macchia d’inchiostro e altri problemi di Shakuntala Devi

Vi propongo tre problemi tratti da Puzzles to Puzzle You, di Shakuntala Devi (2005).

1. La macchia d’inchiostro

La mamma ha spinto una grande tavola rotonda in un angolo della stanza. La tavola tocca entrambe le pareti che formano un angolo retto. Proprio sul bordo della tavola c’è una macchia d’inchiostro che dista esattamente 20 cm da una parete e 22,5 cm dall’altra parete.

Qual è il diametro della tavola?

2. Una croce in una griglia di punti

Venticinque punti sono sistemati su un piano in modo da formare una griglia quadrata 5×5 come mostrato nella figura.

Sei capace di congiungere in sequenza 12 di questi punti con linee rette in modo da disegnare il contorno di una croce greca che abbia 5 punti dentro e 8 punti fuori?

3. Quadrati e triangoli rettangoli

Sei capace di disegnare 2 quadrati e 4 triangoli rettangoli tracciando soltanto 8 segmenti su un foglio?

Risposte & riflessioni

1. La macchia d’inchiostro

Ci sono due diametri validi ma quello accettabile perché corrisponde a una “grande” tavola è 145 cm (oppure 58 pollici, usando i dati in pollici).

L’equazione risolvente è: (r – 20)2 +  (r – 22.5)2 = r2

2. Una croce in una griglia di punti

3. Quadrati e triangoli rettangoli

Pace e bene a tutti.

GfBo

Articoli Correlati

9 Tips From ‘Hi’ to Hookup: tips hook-up on Tinder

Any time you could have aTinder Connecttoday…

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A perfect guide to Tinder hookups

My personal 10 strategies to prepare for meet up(and result in sleep)

6Must-havesyou ought to include in the profile that attract hookups

The number 1 process to create the girl authentically intoYOU

18+ Screenshot instanceswith Tinder connect traces

The2most crucial ideas to know if you would like a hookup

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What to content the girl after an effective hookup

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Obtaining hook ups from internet dating software is an easy feat…. Knowing ideas on how to present your own profile the right way. We’ll guide you for you to start the conversation, get the lady quantity, correct the meetup, and obtain the hookup. All while focussing on becoming real, enjoyable, and respectful.

Is actually Tinder a hookup application?

We’ll allow you to in on a secret…

Tinder is actually a hookup applicationif you like it to be.

Although women and men searching for an union might be offered by Tinder besides.

Due to the fact came here searching for tips about hookups, i will not yap about relationships.

That is a Tinder get together guide.

(these pointers in addition work with Bumble, PoF, Hinge, Badoo, and any other texting app.)

But simply you’ve observed it, discover a screenshot of one of the numerous Tinder marriages:

And although you will seldom see aTinder bioalong these lines:

Perhaps not here for something really serious. I simply desire some rapid fun

There are plenty of women on Tinder that are open to an informal fling.

However they will not be as transparent about any of it because’d like.

We’ll let you know how exactly to identify these wily ladies later on in this specific article.

Since the majority of times, you will find some obvious signs that show the woman real objectives:

But let’s beginning at the CORE. Within the next tip I’ll provide you with 2 things need to know if you would like hookups on any internet dating app.

Action no. 1: most critical 2 factors to know

Inside tip, i will show one thing you wish you’ll recognized the day you downloaded Tinder.

As you likely learn, most men are ready to accept hookups.

We view it all the time whenever mentoring customers.

Also the people seeking connections tend to be available for an adventure on the road.

But all of them make same error:

TheyUNKNOWINGLYsend the wrong indicators.

Although they might be finding a hookup, the ladies they truly are conversing with have no clue of these purposes.

The Reason Why?

The girls merely see a profile and bio that labels them as a platonic friend or boyfriend.

And you are unable to blame all of our Tinder brothers.

Most males are afflicted with the massive myth you have to end up being hyper gentle and sweet for women. Basically, the male vast majority feels that ladies dislike everyday sex.

Plot Twist: women are intimate just like you

The result?

Men create the wrong pages.

Users that demonstrate whatever they THINK females want to see.

And end up making the following profile errors:

Nice, cheerful pictures

An overdose ofpettability: images your own newborn nephew, all your family members over Christmas, …

Boyish vacation pictures

A well-behaved profile book

Signs and symptoms of a successful, healthy life

And it does not only conclude here.

The anti-casual intercourse opinion also infects the way guys text women.

With regards to texting, misguided men make next blunders:

Wondering boring interview-style concerns

Completely unneeded usage of emojis

Long aimless conversations

Fake get-to-know-you topics like ‘her day’

Consider, do you think these users and traces get girls in the state of mind for a Tinder hookup?

I want to respond to that obtainable just in case you’re nevertheless not sure:

No, they do not. Maybe not in the slightest.

It’s your choice showing her the MANLY side.

You need to be delivering a definite sign that says you might be hookup material.

And that’s exactly what i will coach you on in this post.

We are starting with your hookup messages and outlines.

And additional down we are going to handle your own profile.

Step #2: Tinder hook up openers

Time for you supply you with a attach openers.

And perhaps shock a story pose.

In the past tip, i recently told you to move far from aimless talk.

When you need to hook-up, you want to supply your self with texts which are funny, teasing, and also challenging

Here is a typical example of a guy protecting their virginity:

It looks like woman of this screenshot is actually much more prone to get laid than our virgin buddy.

Simply to ensure you won’t ever replicate their errors, let us rapidly evaluate his messages:

This is basically thepeasant opener. The ultimate show of not enough creativity. Its rumored to place even more girls to sleep thanmelatonin.

When she requires him what’s going on, he states ‘nothing’. He has absolutely nothing happening. Absolutely nothing happens in their life, I guess. He then follows it with several abbreviations.

Holy Idea:

Among the many quickest ways to frighten adequate women is to use childish abbreviations, bad spelling, and incorrect sentence structure.

And finally, he hits this lady with a compliment:

I like the name Nikki have no idea exactly why

He loves her title. Cool.

Nothing like she must try to get it. As she politely explains.

Chances are, odds of him obtaining an answer have gone all the way down by about 69per cent.

The exact opposite side of the spectrum can also be very real.

Men making it specific the things they’re after:

Chance for achievements?

Depends upon your own profile but most likely somewhere around 0.8%

Let Us see a Tinder hook-up line that really does supply the lady an idea of what you are after…

…without being hyper humdrum or as well direct:

And her response is a guy’s wet fantasy.

But i’m going to be truthful to you:

A response like this is a rarity.

And while we agree that you wish to telegraph what you are after, thestart of discussionis not the greatest time for significant honesty.

Here is the goal of your opener:

Break the ice and start a conversation.

And here is the twist:

Get together openers don’t have the highest response rate.

They just you should not.

Consider use an opener that DOES have numerous responses, and contributes to the hookup component afterward?

Holy Tip:

The goal of very first text is to find a reply and begin a conversation.

There is one text that performs this better than any.

My Clickbait Opener.

I’m not exaggerating once I say that I get multiple emails weekly with dudes thanking myself with this opener.

In addition to the opener, you also get complimentary access to my key movie.

In which you’ll see myself detailing precisely how to use this icebreaker, and things to text after that.

Plus, you will definately get 7 screenshot instances combined with several bonus recommendations.

Visit this site attain access immediately.

Thank me later.

Or you shouldn’t thank me personally anyway.

Because of the entire connect opener misconception demolished, why don’t we look at the messages to transmit AFTER damaging the ice.

Because following opener is where obtain this lady thrilled for hookup.

Action number 3: Tinder hookup traces

Today, i’ll demonstrate  genuine texts that got guys put and messages that got dudes unrivaled.

But basic circumstances initial.

To seduce some one, and then have an effective Tinder hook-up talk, it is advisable to know that the fundamentals nevertheless apply.

You’re a guy that likes women.

She is a girl that loves guys.

You both enjoyed one another’s profile. So appearances do not be seemingly problems.

Now before she requires“wanna bang?”, which she’ll 99percent of that time period do in Method subtler steps, there is yet another thing you should do:

You should not screw up the talk.

Listed here is a fascinating strategy from a female.

In the place of dull or boring the woman match with horrible classics like:

Hey

Just how are you currently? ????

What now ? for work?

Exactly how was actually your entire day?

What are you undertaking?

She applies to the murder:

Keep in mind that she doesn’t instantly try for the number.

There’s an imaginative accumulation.

She makes it feel like absolutely a real computer problem that she requires help with.

And I also don’t know about you, but about 69per cent of men happen contacted strictly for his or her computer and IT skills before.

Then… storyline pose!

She goes from just using you as a no cost helpdesk, to complimenting you. Right away followed by inquiring your number.

The man is amazed by the woman brilliant trap, and most likely immediately provided his digits.

One slightdetail:

The male is ten instances easier than women regarding hookups.

As we’ve authorized of the woman looks, we simply wish the shortest route toward vayjayland.

Ladies, having said that, run a complete list:

Perform I Believe comfy?

Will I be safe?

Will it be awkward?

Is actually he polite?

Would personally i think drawn to their individuality?

And though the next guy is incredibly onward, no females is ever going to need to ask herself:

“really does he want a hookup, or a reliable union?”

His opener is actually straight to the point

(and stolen out of this renowned movie world:)

Also interesting about his hook up discussion, is that he starts awesome sexually by stating he is here toclap face.

(that i cannot suggest. Indeed certainly one of mytexting guidelinesisnever ever immediately sexualize in your opener.)

But, whenever she defuses his attempt at sexualizing by claiming:

I actually have actually Capri-sun

The guy does not make an effort to sway their, in fact, he does the contrary. The guy lets it be. The guy walks away and then he claims:

I guess Really don’t require the face subsequently

Which is the interesting part.

Look at her reply:

We mean… there’s always both ????

From deflecting the sexual feeling to proposing it.

What this person does very well, and do just as well, is quitede-escalatingin order to elevate.

Ever experienced a situation where someone confirmed interest in you over an extended duration?

And suddenly, that individual actually curious anymore?

For manyphucked upexplanation, it is extremely likely that their disinterest inside you abruptly enables you to interested in all of them.

Now we’re not planning plunge into deep information and brabble around 30 minutes about the reason we pursue those who overlook united states. Instead, I’m going to tell you thatdisinterest also raises appeal for a while.

As a matter of fact, that’s what took place in the last screenshot example.

Do remember that there has to be SOME intrigue inside you to help make this work. You simply can’t program fascination with someone who dislikes you, subsequently take away your own interest and expect these to abruptly want you.

Maybe not attending happen.

Anyway, one thing is for certain. In case your aim is actually a hookup, you should get the woman wide variety sooner than afterwards.

Why?

Because if you construct the cards available, and she doesn’t like exactly what she views, there’s a reasonable opportunity you will definately get unequaled.

Particularly if your own ways of attraction are like the past gent’s approach.

Thus simply take the lady number, and capture the risky connect traces here.

Your own undercover Tinder score will many thanks.

Whatever laughs you don’t want to exposure sending on online dating application.

Action no. 4: Asking this lady number

In this tip, you receive three ways to get the woman quantity…

…Plus 3 explanations why you need to obtain the wide variety ASAP.

I simply said that by getting the girl number, you safeguard your self from unnecessary unmatches. Unmatches that probably hurtyour ELO rating.

Here are two different reasons to get her wide variety earlier than later:

Tinder is FULL of absolutely CLUELESS guys. It is possible to be noticed throughout the software, but you’re nonetheless in her own Tinder inbox. That is the spot in which she becomes swarmed withpeasant openersalong with other boring messages.

The woman iMsg, WhatsApp, whatever inbox using the woman quantity, conversely, is actually somewhere for family and friends. And occasionally men that caused it to be after dark online dating application. Its an even more comfortable and honest place than the woman dating software email.

Katie has experienced it with Tinder’s populace of clueless men.

Today allow me to supply 3 ways to get the lady wide variety.

Beginning with one it is possible to blatantly take and copy-paste without using just one head cellular.

Everything starts with an easy concern:

Find out about it:

The same as inside the screenshot, you will determine if your match has actually good wit, or if she also, likes not using just one head cell.

A more chosen response is:

I’ve have got to provide to you personally. Which was sleek. What about you may well ask my personal quantity initial?

As well as the rest is actually history.

Next approach? Let us get!

Hello, are you presently good with puzzles?

She replies with a yes, or occasionally, or no, or anything.

And then you go:

Really I’m caught on this one, are you able to help you?

(___) ___ – ____

Right after which ideally, she wants your own idea and replies something such as:

Escape Tinder, hello WhatsApp!

Of course, addititionally there is the method that people saw in step three. That cheesy but sweet opener a lady applied to men.

Or, a bonus way… you could get her wide variety without gimmicks. And merely inquire about her number on any peak from inside the talk.

Let’s carry on chatting over WhatsApp if you don’t worry about.

Or the most popular means… only give her your wide variety. Listed here are two fresh screenshot instances:

My match and I also were bantering about one thing additionally the topic fizzled on.

Its my personal job to changeover into new things.

Or… for those who have a good profile that inspires your fits, she will be able to get this to change.

Just what actually took place here.

Which means you lived in a cool storage field for a time, tell me about this

An Account Really Don’t mind revealing, but it’s some lengthy to type…

The most wonderful possibility to get this lady wide variety, by giving her your own quantity.

I’ll do this over a vocals memo, if you don’t mind.

As well as the rest is actually history.

Another screenshot exemplory case of a Tinder attach conversation where I get the quantity?

First and foremost, remember what we spoken of in Step no. 3?De-escalation?

A mixture of de-escalation and self-deprecating wit is at work right here.

And it’s working wonders.

This girl is actually enjoying the talk, now virtually requests for more interest:

I consent she does it in a brattish and spoiled fashion, but that’s good.

(ladies conveniently get away with this sort of conduct on internet dating apps. Since the majority people males, unfortuitously, hop through hoops for them in the breeze of the thumb.)

So, I get the lady quantity giving her my personal figures.

This might be in addition amongobtaining the girl wide variety at a top during the discussion.

Btw, the side-effect of offering your own number and creating HER text YOU, usually she is already trading more. She’s to set up your time and effort to save your quantity and add a reputation. IN ADDITION, she’s to begin contact in the brand new platform.

Alright, i recently offered you 5 methods for getting the girl quantity.

By now you will end up texting overWhatsApp, iMsg, Wechat, Telegram, Viber, whatever.

The time to inquire about her out is virtually.

After several texts straight to her wide variety, you can usually safely ask the girl on.

Step number 5: Ask their away over book

Let’s just take a simple split from reading and merely enjoy a video alternatively.

All you need to know to inquire about the lady around over book, transmitted to your head within just five full minutes:

In Case You Are seeing this on the cellphone and also you don’t have limitless data…

…then lol just what cavern will you be residing in bro, you absolute primate.

Only kidding.

Next simply keep reading and save the movie for later OR, available my post about the subject in another tab.

You might get my personal guidelines onhow-to ask a female out over bookhere.

Today, {once you’ve|once you havehttp://hook-up-dating.com/

Sette donne matematiche per sette ispirazioni (2)

Dopo la prima parte introduttiva e l’omaggio a Maryam Mirzakhani, in questa seconda parte vi racconto di altre tre donne matematiche a cui devo moltissimo e che ogni giorno ci possono ispirare nel nostro lavoro di insegnanti.

Emma Castelnuovo

Grazie a Emma Castelnuovo perché ci insegna a condurre il nostro lavoro come una continua ricerca didattica.

Emma Castelnuovo (1913-2014), matematica italiana di cultura ebraica.

Un libro tradizionale comincia dalle definizioni e dai concetti generali ma non dimentichiamoci che ciascuna delle nostre definizioni è il risultato di un lavoro durato secoli.
Io non do nessuna definizione, l’alunno dovrà sentire lui stesso la necessità delle definizioni, dovrà formulare lui stesso le definizioni.

In tutta la mia vita da studente, tranne nei rari casi in cui ho incontrato un Grande Maestro, sono stato esposto a una Matematica suddivisa in discipline perfettamente organizzate.
Si cominciava con gli assiomi e per il resto ogni teoria si sviluppava in una sequenza di definizioni e teoremi. C’era qualche esempio semplice e seguivano esercizi complicati. Dal generale al particolare, dalla teoria alla pratica. Forse è così anche oggi.
Mancava la spiegazione del perché l’organizzazione era proprio quella e non un’altra. Cioè mancava il senso di ciò che stavo facendo. Ma soprattutto nessuno mi raccontava come si inventa la matematica.
Mi sentivo come uno che vuole imparare ad andare in bicicletta e per risposta riceve un corso sulla struttura della bicicletta: ruote, manubrio, catena di trasmissione, pedali. Ma non avevo il coraggio di rivelare questo disagio, anzi, mi sentivo persino in colpa per averlo.
Diventato a mia volta insegnante stavo per ripetere lo stesso schema con i miei alunni quando per fortuna mi capitarono tra le mani alcuni libri di Emma Castelnuovo. Emma ha avuto il coraggio di dire che quella impostazione è sbagliata e di mostrare quella giusta.
Emma è una Grande Maestra.

Ora, se una disciplina mi viene somministrata dal generale al particolare, a partire da leggi evidenti, da definizioni e da concetti semplici, non ho la sensazione di poter dare io un contributo a questo studio.
Il mio maestro potrà suggerirmi problemi e applicazioni di quanto ha spiegato, e io potrò con entusiasmo cercare di risolverli, ma, badiamo bene, è un ardore che finisce subito dopo risolto quel problema e rimane legato a quel determinato capitolo, ma non ho l’impressione di essere io a creare tutta la geometria e il susseguirsi dei problemi e dei capitoli.

Tratto da Emma Castelnuovo, Geometria intuitiva, per le scuole medie inferiori, Carrabba, 1948.

Shakuntala Devi

Grazie a Shakuntala Devi perché ci ispira il grande amore per i numeri e la forte determinazione nel fare tanti, ma proprio tanti esercizi.

Shakuntala Devi (1929-2013), matematica indiana.

All’età di tre anni mi innamorai dei numeri.
Era pura estasi per me fare addizioni e ottenere il risultato giusto.
Nei numeri trovavo una sicurezza emotiva: due più due faceva sempre quattro e avrebbe sempre fatto quattro – in qualunque modo fosse cambiato il mondo.

Tratto da Shakuntala Devi, Figuring. The Joy of Numbers, 1977.

Shakuntala Devi riusciva a fare mentalmente calcoli che sembrano assolutamente impossibili per un umano.
Per esempio, in una prova calcolò il prodotto di due numeri di 13 cifre in 28 secondi.

7.686.369.774.870 × 2.465.099.745.779 = 18.947.668.177.995.426.462.773.730

Shakuntala voleva che i numeri su cui operare le fossero dati SENZA i punti separatori delle migliaia, cioè così:

7686369774870 × 2465099745779 = ?

Diceva che i separatori delle migliaia spezzano il numero in modo artificiale (negli Stati Uniti si usano le virgole come separatori delle migliaia).

In un’altra prova estrasse la radice 23-esima di un numero di 201 cifre in 50 secondi.
Il numero n era:
n = 916748676920039158098660927585380162483106680144308622407126516427934657040867096593279205767480806790022783016354924852380335745316935111903596577547340075681688305620821016129132845564805780158806771E la sua radice 23-esima:

Provate soltanto a leggere il numero di partenza e farvene un’immagine mentale!

Ma, a parte questi casi limite, per lei era normale estrarre mentalmente radici cubiche come questa in pochi secondi.

C’è una grande ricchezza nei numeri: possono prendere vita, cessare di essere simboli scritti sulla lavagna e guidare il lettore in un mondo avventuroso dove i calcoli sono entusiasmanti anziché noiosi.

Tratto da Shakuntala Devi, Figuring. The Joy of Numbers, 1977.

Lo psicologo Arthur Jensen studiò accuratamente le prodigiose abilità di Shakuntala e le confrontò con quelle di altri studenti esperti e allenati ma riuscì a spiegarle solo in parte.
Ecco alcune delle sue conclusioni:

Shakuntala, a parte la sua fenomenale abilità, aveva una personalità socievole, simpatica, comunicativa, sicuramente non era un autistic savant;
fin da piccola sviluppò un amore per i numeri che la portò a esercitarsi costantemente ogni giorno e a sviluppare una notevole capacità di concentrazione;
aveva costruito immagini mentali dei numeri diverse da quelle usate dalla maggior parte di noi;

Per approfondire l’argomento potete leggere l’articolo originale: Arthur R. Jensen, Speed of Information Processing in a Calculating Prodigy, University of California, Berkeley, INTELLIGENCE 14, 259-274, 1990.
Shakuntala Devi scrisse almeno sei libri di  giochi ed esercizi matematici e qui mi piace citare quello in cui ella racconta il suo amore per i numeri e spiega alcune delle sue tecniche di calcolo:Shakuntala Devi, Figuring. The Joy of Numbers, Harper & Row, 1977.

A proposito della moltiplicazione, la cosa più importante da sapere è quella di NON adottare automaticamente un solo metodo. Bisogna invece osservare i numeri e decidere quale dei molti metodi che vi spiegherò è il più veloce e funziona meglio.

Tratto da Shakuntala Devi, Figuring. The Joy of Numbers, 1977.

Vi propongo qui tre problemi tratti da Puzzles to Puzzle You, Shakuntala Devi, 2005.

Suor Mary Kenneth Keller

Grazie a Suor Mary Kenneth Keller per far capire davvero ai nostri alunni cos’è il “coding” e come esso ci può insegnare l’umiltà e la pazienza.

Suor Mary Kenneth Keller B.V.M. (1913-1985), monaca cristiana, informatica statunitense.

Il computer mi ha aiutata a esercitare due virtù: l’umiltà, perché gli errori non sono della macchina ma del programmatore, e la pazienza, nelle infinite operazioni di debug, nel cercare le linee di codice contenenti errori e correggerle.

Nei lontani anni Ottanta riuscii finalmente a comprarmi un VIC 20. Era un vero computer, piccolo come una tastiera e si poteva collegare al televisore di casa. Era quello più economico ma costava come un mese del mio stipendio da insegnante.
Mi entusiasmò e decisi di usarlo a scuola nelle mie lezioni per insegnare un po’ di programmazione (oggi la chiamano coding). A quel tempo i personal computer si potevano usare SOLO per fare coding e l’unico linguaggio disponibile era il BASIC. Se volevi che il computer facesse qualcosa dovevi scrivere il programma (oggi lo chiamano app).
Credevo di essere all’avanguardia ma non conoscevo il mio grande debito nei confronti di una suora: suor Mary Kenneth Keller, delle Suore della Carità della Beata Vergine Maria.
Fu lei che collaborò con i professori John Kemeny e Thomas Kurtz allo sviluppo del linguaggio BASIC nel 1964.
L’interesse principale della sua vita rimase sempre quello dei computer come supporto all’istruzione e alla formazione di personale capace di sfruttare le potenzialità della rivoluzione informatica.
A presto per la prossima puntata!

Stencil: rielaborazione grafica di Gianfranco Bo

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