MIT-McGovern-Institute

Major grant to study brain basis of autism and dyslexia

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Quick note: Recent announce­ment that adds hope to the under­stand­ing and future treat­ment of autism and dyslex­ia: MIT’s McGov­ern Insti­tute researchers award­ed $8.5m to study brain basis of autism and dyslex­ia. Quote:

- “Two researchers at MIT’s McGov­ern Insti­tute for Brain Research will head an ambi­tious new project to study the ori­gins of autism and dyslex­ia, sup­port­ed by a $8.5m grant from the Elli­son Med­ical Foun­da­tion. The project lead­ers, Nan­cy Kan­wish­er and John Gabrieli, are promi­nent experts in neu­roimag­ing and human brain development.”

Link: McGov­ern Insti­tute for Brain Research at MIT

Math Brain Teaser: Concentric Shapes or The Unkindest Cut of All, Part 2 of 2

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If you missed Part 1, also writ­ten by puz­zle mas­ter Wes Car­roll, you can start there and then come back here to Part 2.

Con­cen­tric Shapes:
The Unkind­est Cut of All, Part 2 of 2

Dif­fi­cul­ty: HARDER
Type: MATH (Spa­tial)
Vitruvian Man

Ques­tion:
Imag­ine a square with­in a cir­cle with­in a square. The cir­cle just grazes each square at exact­ly four points. Find the ratio of the area of the larg­er square to the smaller.

In this puz­zle you are work­ing out many of the same skills as in Part I: spa­tial visu­al­iza­tion (occip­i­tal lobes), mem­o­ry (tem­po­ral lobes), log­ic (frontal lobes), plan­ning (frontal lobes), and hypoth­e­sis gen­er­a­tion (frontal lobes).

Solu­tion:
Two to one.

Expla­na­tion:
Draw the small­er square’s diag­o­nal to see that the the small­er square’s diag­o­nal is the diam­e­ter of the cir­cle. Divide the larg­er square into two equal rec­tan­gu­lar halves to see that the larg­er square’s side is also the diam­e­ter of the cir­cle. This means that the small­er square’s diag­o­nal equals the larg­er square’s side. (Or, if you pre­fer, sim­ply rotate the inner square by 45 degrees.) As we’ve seen in the ear­li­er puz­zle “The Unkind­est Cut Of All,” the area of the small­er square is half that of the larg­er, mak­ing the ratio two to one.

 

More brain teas­er games:

Math Brain Teaser: The Unkindest Cut of All, Part 1 of 2

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In hon­or of Math­e­mat­ics Aware­ness Month, here is anoth­er math­e­mat­i­cal brain ben­der from puz­zle mas­ter Wes Carroll.

The Unkind­est Cut of All, Part 1 of 2

Dif­fi­cul­ty: HARD
Type: MATH (Spa­tial)
Square

Ques­tion:
The area of a square is equal to the square of the length of one side. So, for exam­ple, a square with side length 3 has area (32), or 9. What is the area of a square whose diag­o­nal is length 5?

In this puz­zle you are work­ing out your spa­tial visu­al­iza­tion (occip­i­tal lobes), mem­o­ry (tem­po­ral lobes), and hypoth­e­sis gen­er­a­tion (frontal lobes).

Solu­tion:
12.5

Expla­na­tion:
I am espe­cial­ly fond of these two ways to solve this problem:

1. Draw the right tri­an­gle whose hypotenuse is the square’s diag­o­nal, and whose two legs are two sides of the square. Then use the Pythagore­an The­o­rem (a^2 + b^2 = c^2) to solve for the length of each side. Since two sides are equal, we get (a^2 + a^2 = c^2), or (2(a^2) = c^2) ). Since c is 5, 2(a^2) = 25, mak­ing a^2 equal to 25/2, or 12.5. Since the area of the square is a^2, we’re done: it’s 12.5.

2. Tilt the square 45 degrees and draw a square around it such the the cor­ners of the orig­i­nal square just touch the mid­dles of the sides of the new, larg­er square. The new square has sides each 5 units long (the diag­o­nal of the small­er square), and it there­fore has area 25. How­ev­er, a clos­er inspec­tion reveals that the area of the larg­er square must be exact­ly twice that of the small­er. There­fore the small­er square has area 25/2, or 12.5.

You can now go on to Con­cen­tric Shapes: The Unkind­est Cut of All, Part 2 of 2

 

More brain teas­er games:

Brain Teaser: Dr. Nasty’s Giant Cube

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Here is anoth­er mind-ben­der cre­at­ed by Wes Car­roll for the Sharp­Brains readers.

Pre­sent­ing …
Dr. Nasty’s Giant Cube

Dif­fi­cul­ty: HARDER
Type: HYBRID (Logic/Spatial)

Ques­tion:
The dia­bol­i­cal Dr. Nasty has turned his Growth Ray on a per­fect cube that used to mea­sure one foot on a side. The new larg­er cube has twice the sur­face area of the orig­i­nal. Find the vol­ume of the larg­er cube.

cube brain teaser

Click to read Hint #1.

Click to read Hint #2.

Click to read Hint #3.

Click to read Hint #4.

Click to read the Solu­tion and Expla­na­tion.