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{{about|the mathematical notion|its applications in geodesy|great-circle distance|fictional interstellar organization called Great Circle|Andromeda (novel)}}
Each of these women is following a different elimination diet - but whose is really the healthiest? We asked top nutrition therapist Ian Marber to put their regimes to the test�<br>Who has the healthiest diet? Find out what (from left) What Amy Wilson, Nicole Mowbray and Danni Davis eat<br><br><br>LOW CARB<br><br>Jane Mullen, 33, is an executive assistant and lives in Sussex<br>Size 8 Jane eats less than 1,000  funny pranks on teachers during class calories some days - half her recommended intake - and consumes nothing until lunchtime. The smoker also has one or two glasses of wine on Fridays and Saturdays.<br>Height: 5ft 9in<br>Weight: 9st 3lb<br>BMI: 19<br>Dress size: 8<br><br><br>DIET SNAPSHOT<br>THURSDAY<br>Lunch Takeaway tuna salad (with boiled egg, edamame beans, leaves) <br>Dinner Baked chicken and salad (lettuce, cucumber, onion, red cabbage)<br>Drinks 2 cups of coffee with skimmed milk, Berocca [vitamin drink], 2 pints of water<br><br>FRIDAY<br>Lunch Tuna and cannellini beans, red onion and rocket with a mustard and olive oil dressing <br>Dinner Steak with asparagus, spinach and harissa carrots (blanched carrots with a dressing of harissa paste) <br>Drinks 2 cups coffee with skimmed milk, Berocca, glass of white wine, 2 pints of water <br><br>SATURDAY<br>Lunch Chicken superfood salad<br>Dinner Homemade Mexican beef stew with avocado, iceberg lettuce and grated cheese<br>Snack Mini Cadbury�s Creme Egg<br>Drinks 2 cups of coffee with skimmed milk, Berocca, 2 pints of water, 2 glasses of white wine<br><br>Ian says:<br>The first thing that strikes me is that Jane doesn�t eat very much. In a whole day, she�s consuming what an active man would eat as a snack, not enough to keep a grown woman energised. On some days I would estimate it�s less than 1,000 calories: a grown woman should ideally consume 1,800-2,000 calories a day depending on her age, size and activity level.<br>Having nothing to eat until lunchtime and existing on coffee and cigarettes [Jane is a smoker] means she is relying  funny fail compilation on these for her energy. We like to think that the body will use its fat stores to provide energy when we�re not eating food,  [http://goo.gl/cPYUZA funny pranks 2014] but it�s often not the case. If you�re a stressed person, a smoker or a coffee drinker (or all three), then the body often releases adrenalin to meet its energy needs instead of burning fat. In the short term, this means you�ll have a small appetite and be more prone to feelings of stress, but in the long term, living this way raises your risk of adrenal exhaustion and, rarely, conditions such as Addison�s disease (a disorder of the adrenal glands). <br>Jane should aim to eat a small amount in the morning, within an hour of waking up, before her adrenalin and the caffeine kicks in. I don�t necessarily agree with Jane�s very low carb intake - I think having some carbs in the morning would be good for her. Porridge is an obvious suggestion, but even if she just ate a few blueberries and some almonds she would provide her body with some vitamin C and fibre.<br>As a smoker, Jane needs far more vitamin C than she is getting and more nutrients in general - just one Berocca a day is not enough. I would be surprised if Jane meets the recommended daily allowance (RDA) for vitamins, particularly the Bs because they�re often found in whole grains and her diet is mostly grain-free. <br>VERDICT: I would caution Jane that this type of diet needs to be �low carb� not �no carb� - she needs to eat more and an easy way to do this is to start the day with breakfast.<br><br>Jane says:<br>Going low carb wasn�t something I consciously decided to do, although I am keen to eat healthily. I suppose it�s like anything - you get into a pattern. I rarely feel hungry in the mornings. I live by myself and find that potatoes and bread go off before I can finish them so I tend not to buy them and I�ve never liked pasta. I do like brown rice though, so perhaps I could reintroduce it.<br>More... <br>Crohn's sufferers share selfies showing their colostomy bags after woman's bikini photo exposing hers went viral<br><br>The Loneliness of Lulu: Struggling with getting older. The heartbreak of her failed marriages. And waking in the night worrying about being a burden... the most revealing - and saddest - interview Lulu has ever given...<br><br>My acne nightmare, by Samantha 'I'm so beautiful' Brick: She claimed she was hated for being too attractive, but now, Samantha admits she's not so perfect after all<br><br>LOW FAT<br>Amy Wilson, 24, works in PR and lives in Sheffield <br><br>8st 11lb Amy tries her best to eat healthily during the week - and, on the whole, does so successfully - although she tends to snack at the weekends. She also drinks plenty of water and coffee or tea. <br>Height: 5ft 3in<br>Weight: 8st 11lb<br>BMI: 21.7<br>Dress size: 10 <br><br><br>DIET SNAPSHOT<br>THURSDAY<br><br>Breakfast Porridge with semi-skimmed milk<br>Snack Banana, � avocado<br>Lunch Egg sandwich <br>Snack Couple of bites of banana<br>Dinner Homemade pork and veg casserole with a jacket potato; flavoured low-fat yoghurt<br>Drinks 1 instant coffee with semi-skimmed milk, 5 glasses of water, 1 herbal tea<br><br>FRIDAY<br>Breakfast Porridge with semi-skimmed milk<br>Snack Banana<br>Lunch Spinach, tuna, tomatoes, pinto beans, � avocado, hot sauce; flavoured low-fat yoghurt<br>Snack 2 rice cakes<br>Dinner Homemade spaghetti bolognese with wholemeal spaghetti; berry frozen yoghurt<br>Drinks 1 instant coffee with semi-skimmed milk, 4 glasses of water, 1 herbal tea<br><br>SATURDAY<br>Breakfast Poached egg, courgette bread, halloumi, tomatoes, rocket, tomato relish<br>Snack Couple of bites of custard doughnut<br>Lunch Packet of sushi<br>Snack Handful of milk chocolate buttons<br>Dinner Turkey breast, leek and cabbage, sweet potato; flavoured low-fat yoghurt<br>Drinks 1 instant coffee with semi-skimmed milk, 1 coffee with full-fat milk, 3 glasses of water, 1 herbal tea<br><br>Ian says:<br>Amy�s diet is, on the whole, pretty good. It�s low in saturated fat yet includes some of the good fats (such as avocado) and lean protein (such as turkey and eggs). It has a slightly high GI though, caused by, for example, the spaghetti, sushi and sandwich (foods with a high glycaemic index quickly convert to sugar in the body, which can lead to energy slumps), which isn�t ideal. But on the plus side, she is eating good food - the only �processed� food is her sugary flavoured yoghurt. She would be better off having a plain one instead. <br>However, Amy should eat more protein in the morning. Adding walnuts to her porridge would give her a good hit of omega 3, which has been shown to improve heart and brain health and reduce anxiety levels. Like many of us, Amy eats slightly more processed food and sugar at the weekends - although eating a little bit of doughnut and a few chocolate buttons hardly counts as bingeing.<br>Often when people eat to a �theme� such as low fat, they just eat foods that tick their boxes and don�t look at what else they contain. For instance, Amy eats sushi - which is low in fat, but high in sugar. People who eat low-fat foods often find themselves eating more sugar, which is something Amy needs to keep an eye on. Although she is slim, high-sugar diets can play havoc with the body�s hormonal responses and increase feelings of tiredness, irritability and mood swings. <br>VERDICT: Overall, Amy�s diet is pretty good. She hasn�t fallen into the trap that many low-fat eaters can - namely that they don�t differentiate good fats from bad; they look at fats such as those in nuts and avocado as solely calorific and are blinded to their nutritional value.<br><br>Amy says:<br>I am health-conscious and make a big effort to eat healthily during the week. It�s easy to stick to low-fat food when I�m sitting at my desk without temptations, but at the weekends, I feel like it�s my treat time. Ian�s suggestion of eating nuts as a way of getting protein into my diet is a good one, but my boyfriend is severely allergic to them so I tend not to have them in the house. Perhaps I could put some seeds on my porridge instead - it�s definitely something I�ll look into.<br><br>LOW PROTEIN (vegetarian)<br>Danni Davis, 35, owns fitness franchise Boxit 2 The Beat and lives in Greater Manchester <br><br>Danni, who has been a vegetarian for 25 years, has been advised to be more consistent with eating protein - and cutting down on indulgent foods. She also enjoys milkshakes and alcohol.<br><br>Height: 5ft 7in<br>Weight: 11st 5lb<br>BMI: 25<br>Dress size: 12<br><br>DIET SNAPSHOT<br>THURSDAY<br><br>Breakfast 2 pieces of fruit toast with olive spread<br>Lunch Mushroom risotto soup<br>Snacks 2 plums, Cadbury�s Mini Roll, small bag of mini eggs<br>Dinner Prawn crackers, deep fried tofu in black bean sauce with vegetables, steamed rice, edamame beans <br>Drinks 1 coffee with semi-skimmed milk and sweetener, 4 glasses of water, 1 beer, sparking water<br><br>FRIDAY <br>Breakfast 2 plums, 1 tangerine<br>Lunch Sweet potato, squash, feta burrito, � corn on the cob<br>Snack Cornflake cake<br>Dinner Tofu and vegetables, steamed white rice<br>Drinks Sparkling water, 1 margarita cocktail, 1 beer<br><br>SATURDAY <br>Breakfast Scrambled eggs, 2 pieces of sourdough toast<br>Lunch Soft-boiled egg salad with mushrooms, sun-dried tomatoes, olive oil dressing,4 mozzarella sticks<br>Dinner � mushroom spring roll, 2 pieces of Chinese fried cheese, mushroom and date casserole, steamed rice, meringue bombe with mango coulis and lychee sorbet<br>Drinks Soya cappuccino, milkshake, 1 glass champagne, 1 vodka/soda fresh lime, 4 glasses of red wine<br><br>Ian says:<br>Many vegetarian diets are low in protein, which means you�re almost always going to be eating higher GI foods that the body quickly converts to energy. This doesn�t necessarily mean you eat more sugar, but more sugars, plural, by which I mean more grains. <br>Protein automatically dampens down the body�s blood glucose levels to stop you feeling hungry and tired. Those eating a high GI/low-protein diet like Danni will experience fluctuations in their blood glucose quite regularly, making them feel frequently fatigued followed by hunger pangs and sugar cravings. <br>Danni also eats a lot, which I would put down to fluctuating glucose levels that make her hungry more quickly. Choosing a low-protein food  funny vines 2014 at this time - as many veggies do - starts the cycle off again. Vegetarians should up their fat intake from sources such as cheese because they�re not getting it from meat.<br>Although Danni�s dinner on day one is quite good, I would advise her to be more consistent about eating protein - she really needs to seek it out. Her fruit toast in the morning, for example, is sugary. Instead, Danni could have granary toast with some sugar-free peanut butter for protein. Nuts are also great for vegetarians. <br>VERDICT: Danni needs to incorporate more protein into her diet and try to be a bit more careful at weekends - a lot of the more indulgent foods she consumes, such as the milkshake, meringue and alcohol, have little or no nutritional value. But, on the plus side, Danni is obviously someone who enjoys her food. Her diet seems the most joyful and varied. <br><br>Danni says:<br>I have been a vegetarian since I was ten, simply because I hate the taste of meat. Ian is right, though - I don�t get enough protein, I do eat too much sugary food and I�m often hungry. I�m allergic to nuts so they�re out, but I am going to make an effort to up my intake of seeds and pulses to boost my protein intake.<br>LOW SUGAR<br>Nicole Mowbray, 34, is a writer and lives in London <br><br>Nicole's mostly-homemade diet has been praised as 'ticking every box'. She has dramatically cut down her sugar intake over the past two years, and insists she feels much better for it.<br>Height: 5ft 10in<br>Weight: 11st 7lb<br>BMI: 23.1<br>Dress size: 12<br><br><br>DIET SNAPSHOT<br>THURSDAY<br><br>Breakfast Homemade buckwheat, chia and linseed pot made with almond milk and a few blackberries<br>Lunch Homemade kale and peanut salad with watercress, spinach, rocket, tomatoes and olive oil, salmon, whole yoghurt with pistachios<br>Snack 2 oatcakes with hummus<br>Dinner Calamari, small grilled fillet steak with watercress and tomato salad<br>Drinks 2 cups decaf tea, decaf flat white coffee, 2� litres of water, 1 cup of rose tea, 1 peppermint tea, glass of sparkling water<br><br>FRIDAY<br>Breakfast Shakshuka (eggs baked in tomato) <br>Snack Oat smoothie made with protein powder, rice milk, oats, cinnamon<br>Lunch Half a piece of sourdough with fresh crab <br>Dinner Grilled plaice, green beans and peas<br>Drinks 2 litres water, 1 cup of decaf tea, decaf latte, peppermint tea, 1 glass of red wine<br><br>SATURDAY<br>Breakfast one 5-grain, 5-seed porridge made with water, topped with coconut oil, linseeds and ground almonds<br>Breakfast  epic fail compilation 2014 2 poached eggs, 2 grilled tomatoes, 1 grilled field mushroom<br>Lunch 2 falafel, roasted vegetable galette made with buckwheat flour, quinoa and chickpea salad, small piece of cheese<br>Dinner Grilled tuna steak, stir-fried Asian greens in satay-style sauce (made with no-added-sugar peanut butter), brown rice noodles<br>Drinks 2 cups of decaf tea, 2 litres of water, 1 decaf latte, pot of peppermint tea, glass of milk<br><br>Ian says:<br>This diet ticks every box. It�s mostly homemade and has everything in it. It�s really nutrient dense - that�s not just the individual ingredients but also the food groups. It�s pretty darn good. Although Nicole has cut out something - in her case, sugar - her diet still has lots of variety and that�s key.<br>If you cut out sugar, what you choose in its place is really important. I recently read that Michelle Obama�s chef said that he admired her decision to replace sugar in desserts at the White House with honey. However, it�s a bit of a naive knee-jerk reaction because honey sends blood sugar levels soaring followed by a crash, just like sugar. <br>One of the perils of eliminating something from your diet is that firstly you cut something out without replacing it and secondly you think that as long as you avoid that food - whether it�s sugar as here, or fat - then you�re OK. But that�s not always the case. A vegetarian, for example, wouldn�t have beef and onion crisps because they�re beef, but they may have regular salted crisps. Trying to be healthy in this way can divert the mind; it can be a bit of a red herring.<br>VERDICT: Sugar has been in the news a lot this year and with good reason. Most of us could benefit from cutting back on sweet foods because high-sugar diets can play havoc with the body�s hormonal responses. People who eat a lot of sugar often feel hungry, tired, irritable and anxious. <br><br>Nicole says:<br>Trying to eat healthily is my USP, but it hasn�t always been. Two years ago I ate sugar in some form for every meal, every snack and almost every drink. I was fat and spotty, moody and tired. I worked out that sugar was the culprit and decided to give it up. Gradually I felt more energised and healthier and I am now slimmer, have fewer spots and wrinkles and I sleep better. I do occasionally have a glass of red wine, but I don�t eat much fruit. Eating out is easy too, it�s just all about making the right choices. This isn�t a fad for me, it�s how I want to live the rest of my life.<br>Sweet Nothing - Why I Gave Up Sugar and How You Can Too by Nicole Mowbray is published by Orion, �7.99*<br>Eat Your Way To Lower Cholesterol by Ian Marber, Dr Laura Corr and Dr Sarah Schenker is published by Orion, �16.99*<br>*To order copies for a discounted price with free p&p, contact the YOU Bookshop on 0844 472 4157 or visit you-bookshop.co.uk
 
[[File:Great circle hemispheres.png|thumb|right|A great circle divides the sphere in two equal hemispheres]]
 
A '''great circle''', also known as an '''orthodrome''' or [[Riemannian circle]], of a [[sphere]] is the intersection of the sphere and a [[Plane (geometry)|plane]] which passes through the center point of the sphere, a partial case of a [[circle of a sphere]] where the plane is not required to pass through the center. (A ''small circle'' is the intersection of the sphere and a plane which does not pass through the center.) Any [[diameter]] of any great circle coincides with a diameter of the sphere, and therefore all great circles have the same [[circumference]] as each other, and have the same center as the sphere. A great circle is the largest circle that can be drawn on any given sphere. Every [[circle]] in [[Euclidean space|Euclidean 3-space]] is a great circle of exactly one sphere.
 
For any two points on the surface of a sphere there is a unique great circle through the two points.  An exception is a pair of [[Antipodal point|antipodal]] points, for which there are infinitely many great circles. The minor arc of a great circle between two points is the shortest surface-path between them. In this sense the minor arc is analogous to “straight lines” in [[spherical geometry]]. The length of the minor arc of a great circle is taken as the distance between two points on a surface of a sphere in [[Riemannian geometry]]. The great circles are the [[geodesic]]s of the sphere.
 
In higher dimensions, the great circles on the [[n-sphere|''n''-sphere]] are the intersection of the ''n''-sphere with two-planes that pass through the origin in the Euclidean space '''R'''<sup>''n''+1</sup>.
 
==Derivation of shortest paths==
{{see also|Great-circle distance}}
To prove that the minor arc of a great circle is the shortest path connecting two points on the surface of a sphere, one has to apply [[calculus of variations]] to it.
 
Consider the class of all regular paths from a point ''p'' to another point ''q''. Introduce [[spherical coordinates]] so that ''p'' coincides with the north pole. Any curve on the sphere that does not intersect either pole, except possibly at the endpoints, can be parametrized by
 
:<math>\theta = \theta(t),\quad \phi = \phi(t),\quad a\le t\le b</math>
 
provided we allow φ to take on arbitrary real values. The infinitesimal arc length in these coordinates is
 
: <math>
ds=r\sqrt{\theta'^2+\phi'^{2}\sin^{2}\theta}\, dt.
</math>
 
So the length of a curve γ from ''p'' to ''q'' is a [[functional (mathematics)|functional]] of the curve given by
 
: <math>
S[\gamma]=r\int_a^b\sqrt{\theta'^2+\phi'^{2}\sin^{2}\theta}\, dt.
</math>
 
Note that ''S''[γ] is at least the length of the meridian from ''p'' to ''q'':
 
:<math>S[\gamma] \ge r\int_a^b|\theta'(t)|\,dt \ge r|\theta(b)-\theta(a)|.</math>
 
Since the starting point and ending point are fixed, ''S'' is minimized if and only if φ'&nbsp;=&nbsp;0, so the curve must lie on a meridian of the sphere φ&nbsp;=&nbsp;φ<sub>0</sub>&nbsp;=&nbsp;constant. In Cartesian coordinates, this is
:<math>x\sin\phi_0 - y\cos\phi_0 = 0</math>
which is a plane through the origin, i.e., the center of the sphere.
 
==Applications==
Some examples of great circles on the [[celestial sphere]] include the [[celestial horizon]], the [[celestial equator]], and the [[ecliptic]]. Great circles are also used as rather accurate approximations of [[geodesics on an ellipsoid|geodesics]] on the [[Earth]]'s surface (although it [[shape of the Earth|is not a perfect sphere]]), as well as on spheroidal [[celestial bodies]].
 
==See also==
* [[Rhumb line]]
 
==External links==
* [http://mathworld.wolfram.com/GreatCircle.html Great Circle – from MathWorld] Great Circle description, figures, and equations. Mathworld, Wolfram Research, Inc. c1999
* [http://www.greatcirclemapper.net The Great Circle Mapper] Displays Great Circle flight routes on a map and calculates distance and duration
* [http://www.gcmap.com/ Great Circle Mapper] Interactive tool for plotting great circle routes.
* [http://williams.best.vwh.net/gccalc.htm Great Circle Calculator] deriving (initial) course and distance between two points.
* [http://www.acscdg.com/ Great Circle Distance] Graphical tool for drawing great circles over maps. Also shows distance and azimuth in a table.
* [http://demonstrations.wolfram.com/GreatCirclesOnMercatorsChart/ Great Circles on Mercator's Chart] by John Snyder with additional contributions by Jeff Bryant, Pratik Desai, and Carl Woll, [[Wolfram Demonstrations Project]].
* [http://www.spigolo.altervista.org/ortho/OrthoFirstProblem.html 3D First Problem] {{it icon}} 3D javascript interactive tool ([[Google Chrome]], [[Firefox]], [[Safari (web browser)]]).
* [http://www.spigolo.altervista.org/ortho/OrthoSecondProblem.html 3D Second Problem] {{it icon}} 3D javascript interactive tool ([[Google Chrome]], [[Firefox]], [[Safari (web browser)]]).
 
[[Category:Elementary geometry]]
[[Category:Spherical trigonometry]]
[[Category:Riemannian geometry]]

Latest revision as of 13:11, 30 December 2014

Each of these women is following a different elimination diet - but whose is really the healthiest? We asked top nutrition therapist Ian Marber to put their regimes to the test�
Who has the healthiest diet? Find out what (from left) What Amy Wilson, Nicole Mowbray and Danni Davis eat


LOW CARB

Jane Mullen, 33, is an executive assistant and lives in Sussex
Size 8 Jane eats less than 1,000 funny pranks on teachers during class calories some days - half her recommended intake - and consumes nothing until lunchtime. The smoker also has one or two glasses of wine on Fridays and Saturdays.
Height: 5ft 9in
Weight: 9st 3lb
BMI: 19
Dress size: 8


DIET SNAPSHOT
THURSDAY
Lunch Takeaway tuna salad (with boiled egg, edamame beans, leaves)
Dinner Baked chicken and salad (lettuce, cucumber, onion, red cabbage)
Drinks 2 cups of coffee with skimmed milk, Berocca [vitamin drink], 2 pints of water

FRIDAY
Lunch Tuna and cannellini beans, red onion and rocket with a mustard and olive oil dressing
Dinner Steak with asparagus, spinach and harissa carrots (blanched carrots with a dressing of harissa paste)
Drinks 2 cups coffee with skimmed milk, Berocca, glass of white wine, 2 pints of water

SATURDAY
Lunch Chicken superfood salad
Dinner Homemade Mexican beef stew with avocado, iceberg lettuce and grated cheese
Snack Mini Cadbury�s Creme Egg
Drinks 2 cups of coffee with skimmed milk, Berocca, 2 pints of water, 2 glasses of white wine

Ian says:
The first thing that strikes me is that Jane doesn�t eat very much. In a whole day, she�s consuming what an active man would eat as a snack, not enough to keep a grown woman energised. On some days I would estimate it�s less than 1,000 calories: a grown woman should ideally consume 1,800-2,000 calories a day depending on her age, size and activity level.
Having nothing to eat until lunchtime and existing on coffee and cigarettes [Jane is a smoker] means she is relying funny fail compilation on these for her energy. We like to think that the body will use its fat stores to provide energy when we�re not eating food, funny pranks 2014 but it�s often not the case. If you�re a stressed person, a smoker or a coffee drinker (or all three), then the body often releases adrenalin to meet its energy needs instead of burning fat. In the short term, this means you�ll have a small appetite and be more prone to feelings of stress, but in the long term, living this way raises your risk of adrenal exhaustion and, rarely, conditions such as Addison�s disease (a disorder of the adrenal glands).
Jane should aim to eat a small amount in the morning, within an hour of waking up, before her adrenalin and the caffeine kicks in. I don�t necessarily agree with Jane�s very low carb intake - I think having some carbs in the morning would be good for her. Porridge is an obvious suggestion, but even if she just ate a few blueberries and some almonds she would provide her body with some vitamin C and fibre.
As a smoker, Jane needs far more vitamin C than she is getting and more nutrients in general - just one Berocca a day is not enough. I would be surprised if Jane meets the recommended daily allowance (RDA) for vitamins, particularly the Bs because they�re often found in whole grains and her diet is mostly grain-free.
VERDICT: I would caution Jane that this type of diet needs to be �low carb� not �no carb� - she needs to eat more and an easy way to do this is to start the day with breakfast.

Jane says:
Going low carb wasn�t something I consciously decided to do, although I am keen to eat healthily. I suppose it�s like anything - you get into a pattern. I rarely feel hungry in the mornings. I live by myself and find that potatoes and bread go off before I can finish them so I tend not to buy them and I�ve never liked pasta. I do like brown rice though, so perhaps I could reintroduce it.
More...
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My acne nightmare, by Samantha 'I'm so beautiful' Brick: She claimed she was hated for being too attractive, but now, Samantha admits she's not so perfect after all

LOW FAT
Amy Wilson, 24, works in PR and lives in Sheffield

8st 11lb Amy tries her best to eat healthily during the week - and, on the whole, does so successfully - although she tends to snack at the weekends. She also drinks plenty of water and coffee or tea.
Height: 5ft 3in
Weight: 8st 11lb
BMI: 21.7
Dress size: 10


DIET SNAPSHOT
THURSDAY

Breakfast Porridge with semi-skimmed milk
Snack Banana, � avocado
Lunch Egg sandwich
Snack Couple of bites of banana
Dinner Homemade pork and veg casserole with a jacket potato; flavoured low-fat yoghurt
Drinks 1 instant coffee with semi-skimmed milk, 5 glasses of water, 1 herbal tea

FRIDAY
Breakfast Porridge with semi-skimmed milk
Snack Banana
Lunch Spinach, tuna, tomatoes, pinto beans, � avocado, hot sauce; flavoured low-fat yoghurt
Snack 2 rice cakes
Dinner Homemade spaghetti bolognese with wholemeal spaghetti; berry frozen yoghurt
Drinks 1 instant coffee with semi-skimmed milk, 4 glasses of water, 1 herbal tea

SATURDAY
Breakfast Poached egg, courgette bread, halloumi, tomatoes, rocket, tomato relish
Snack Couple of bites of custard doughnut
Lunch Packet of sushi
Snack Handful of milk chocolate buttons
Dinner Turkey breast, leek and cabbage, sweet potato; flavoured low-fat yoghurt
Drinks 1 instant coffee with semi-skimmed milk, 1 coffee with full-fat milk, 3 glasses of water, 1 herbal tea

Ian says:
Amy�s diet is, on the whole, pretty good. It�s low in saturated fat yet includes some of the good fats (such as avocado) and lean protein (such as turkey and eggs). It has a slightly high GI though, caused by, for example, the spaghetti, sushi and sandwich (foods with a high glycaemic index quickly convert to sugar in the body, which can lead to energy slumps), which isn�t ideal. But on the plus side, she is eating good food - the only �processed� food is her sugary flavoured yoghurt. She would be better off having a plain one instead.
However, Amy should eat more protein in the morning. Adding walnuts to her porridge would give her a good hit of omega 3, which has been shown to improve heart and brain health and reduce anxiety levels. Like many of us, Amy eats slightly more processed food and sugar at the weekends - although eating a little bit of doughnut and a few chocolate buttons hardly counts as bingeing.
Often when people eat to a �theme� such as low fat, they just eat foods that tick their boxes and don�t look at what else they contain. For instance, Amy eats sushi - which is low in fat, but high in sugar. People who eat low-fat foods often find themselves eating more sugar, which is something Amy needs to keep an eye on. Although she is slim, high-sugar diets can play havoc with the body�s hormonal responses and increase feelings of tiredness, irritability and mood swings.
VERDICT: Overall, Amy�s diet is pretty good. She hasn�t fallen into the trap that many low-fat eaters can - namely that they don�t differentiate good fats from bad; they look at fats such as those in nuts and avocado as solely calorific and are blinded to their nutritional value.

Amy says:
I am health-conscious and make a big effort to eat healthily during the week. It�s easy to stick to low-fat food when I�m sitting at my desk without temptations, but at the weekends, I feel like it�s my treat time. Ian�s suggestion of eating nuts as a way of getting protein into my diet is a good one, but my boyfriend is severely allergic to them so I tend not to have them in the house. Perhaps I could put some seeds on my porridge instead - it�s definitely something I�ll look into.

LOW PROTEIN (vegetarian)
Danni Davis, 35, owns fitness franchise Boxit 2 The Beat and lives in Greater Manchester

Danni, who has been a vegetarian for 25 years, has been advised to be more consistent with eating protein - and cutting down on indulgent foods. She also enjoys milkshakes and alcohol.

Height: 5ft 7in
Weight: 11st 5lb
BMI: 25
Dress size: 12

DIET SNAPSHOT
THURSDAY

Breakfast 2 pieces of fruit toast with olive spread
Lunch Mushroom risotto soup
Snacks 2 plums, Cadbury�s Mini Roll, small bag of mini eggs
Dinner Prawn crackers, deep fried tofu in black bean sauce with vegetables, steamed rice, edamame beans
Drinks 1 coffee with semi-skimmed milk and sweetener, 4 glasses of water, 1 beer, sparking water

FRIDAY
Breakfast 2 plums, 1 tangerine
Lunch Sweet potato, squash, feta burrito, � corn on the cob
Snack Cornflake cake
Dinner Tofu and vegetables, steamed white rice
Drinks Sparkling water, 1 margarita cocktail, 1 beer

SATURDAY
Breakfast Scrambled eggs, 2 pieces of sourdough toast
Lunch Soft-boiled egg salad with mushrooms, sun-dried tomatoes, olive oil dressing,4 mozzarella sticks
Dinner � mushroom spring roll, 2 pieces of Chinese fried cheese, mushroom and date casserole, steamed rice, meringue bombe with mango coulis and lychee sorbet
Drinks Soya cappuccino, milkshake, 1 glass champagne, 1 vodka/soda fresh lime, 4 glasses of red wine

Ian says:
Many vegetarian diets are low in protein, which means you�re almost always going to be eating higher GI foods that the body quickly converts to energy. This doesn�t necessarily mean you eat more sugar, but more sugars, plural, by which I mean more grains.
Protein automatically dampens down the body�s blood glucose levels to stop you feeling hungry and tired. Those eating a high GI/low-protein diet like Danni will experience fluctuations in their blood glucose quite regularly, making them feel frequently fatigued followed by hunger pangs and sugar cravings.
Danni also eats a lot, which I would put down to fluctuating glucose levels that make her hungry more quickly. Choosing a low-protein food funny vines 2014 at this time - as many veggies do - starts the cycle off again. Vegetarians should up their fat intake from sources such as cheese because they�re not getting it from meat.
Although Danni�s dinner on day one is quite good, I would advise her to be more consistent about eating protein - she really needs to seek it out. Her fruit toast in the morning, for example, is sugary. Instead, Danni could have granary toast with some sugar-free peanut butter for protein. Nuts are also great for vegetarians.
VERDICT: Danni needs to incorporate more protein into her diet and try to be a bit more careful at weekends - a lot of the more indulgent foods she consumes, such as the milkshake, meringue and alcohol, have little or no nutritional value. But, on the plus side, Danni is obviously someone who enjoys her food. Her diet seems the most joyful and varied.

Danni says:
I have been a vegetarian since I was ten, simply because I hate the taste of meat. Ian is right, though - I don�t get enough protein, I do eat too much sugary food and I�m often hungry. I�m allergic to nuts so they�re out, but I am going to make an effort to up my intake of seeds and pulses to boost my protein intake.
LOW SUGAR
Nicole Mowbray, 34, is a writer and lives in London

Nicole's mostly-homemade diet has been praised as 'ticking every box'. She has dramatically cut down her sugar intake over the past two years, and insists she feels much better for it.
Height: 5ft 10in
Weight: 11st 7lb
BMI: 23.1
Dress size: 12


DIET SNAPSHOT
THURSDAY

Breakfast Homemade buckwheat, chia and linseed pot made with almond milk and a few blackberries
Lunch Homemade kale and peanut salad with watercress, spinach, rocket, tomatoes and olive oil, salmon, whole yoghurt with pistachios
Snack 2 oatcakes with hummus
Dinner Calamari, small grilled fillet steak with watercress and tomato salad
Drinks 2 cups decaf tea, decaf flat white coffee, 2� litres of water, 1 cup of rose tea, 1 peppermint tea, glass of sparkling water

FRIDAY
Breakfast Shakshuka (eggs baked in tomato)
Snack Oat smoothie made with protein powder, rice milk, oats, cinnamon
Lunch Half a piece of sourdough with fresh crab
Dinner Grilled plaice, green beans and peas
Drinks 2 litres water, 1 cup of decaf tea, decaf latte, peppermint tea, 1 glass of red wine

SATURDAY
Breakfast one 5-grain, 5-seed porridge made with water, topped with coconut oil, linseeds and ground almonds
Breakfast epic fail compilation 2014 2 poached eggs, 2 grilled tomatoes, 1 grilled field mushroom
Lunch 2 falafel, roasted vegetable galette made with buckwheat flour, quinoa and chickpea salad, small piece of cheese
Dinner Grilled tuna steak, stir-fried Asian greens in satay-style sauce (made with no-added-sugar peanut butter), brown rice noodles
Drinks 2 cups of decaf tea, 2 litres of water, 1 decaf latte, pot of peppermint tea, glass of milk

Ian says:
This diet ticks every box. It�s mostly homemade and has everything in it. It�s really nutrient dense - that�s not just the individual ingredients but also the food groups. It�s pretty darn good. Although Nicole has cut out something - in her case, sugar - her diet still has lots of variety and that�s key.
If you cut out sugar, what you choose in its place is really important. I recently read that Michelle Obama�s chef said that he admired her decision to replace sugar in desserts at the White House with honey. However, it�s a bit of a naive knee-jerk reaction because honey sends blood sugar levels soaring followed by a crash, just like sugar.
One of the perils of eliminating something from your diet is that firstly you cut something out without replacing it and secondly you think that as long as you avoid that food - whether it�s sugar as here, or fat - then you�re OK. But that�s not always the case. A vegetarian, for example, wouldn�t have beef and onion crisps because they�re beef, but they may have regular salted crisps. Trying to be healthy in this way can divert the mind; it can be a bit of a red herring.
VERDICT: Sugar has been in the news a lot this year and with good reason. Most of us could benefit from cutting back on sweet foods because high-sugar diets can play havoc with the body�s hormonal responses. People who eat a lot of sugar often feel hungry, tired, irritable and anxious.

Nicole says:
Trying to eat healthily is my USP, but it hasn�t always been. Two years ago I ate sugar in some form for every meal, every snack and almost every drink. I was fat and spotty, moody and tired. I worked out that sugar was the culprit and decided to give it up. Gradually I felt more energised and healthier and I am now slimmer, have fewer spots and wrinkles and I sleep better. I do occasionally have a glass of red wine, but I don�t eat much fruit. Eating out is easy too, it�s just all about making the right choices. This isn�t a fad for me, it�s how I want to live the rest of my life.
Sweet Nothing - Why I Gave Up Sugar and How You Can Too by Nicole Mowbray is published by Orion, �7.99*
Eat Your Way To Lower Cholesterol by Ian Marber, Dr Laura Corr and Dr Sarah Schenker is published by Orion, �16.99*
*To order copies for a discounted price with free p&p, contact the YOU Bookshop on 0844 472 4157 or visit you-bookshop.co.uk